I have the same problems as you currently. My advice is to take a deep breath and keep a cool head when things turning into a bad way. Keep your friendly fraggers healed, and when in ubers situation try to keep the Uber on the players who are in order: before uber -> while ubered -> just before Uber fades. Keep all flashes equal between all. Follow your designated combo and give heals to those who need it.

If it's a stalemate and you're just spamming, heal the flank when they come for heals/buffs (ideally, when they've taken dmg on the flank they'll back up and wait a bit before coming to you so they can have crit heals) and then resume healing the combo. Make sure no one on the combo is being overly aggressive/peeking when you're buffing the flank.

If a player is on the front lines and getting shot, heal him. If someone is just standing behind and not taking any damage and bitching about not getting healed, tell him to stop bitching and wait a few secs.

If your entire team has shitty health you all need to step back, give up some ground and heal up so you don't get wiped

EDIT:

This is bad advice. You should never flash your entire team equally, that just wastes your uber and makes it super short. If you're just going for an uber trade and you want to force the other team, you should focus on a solo uber. Only flash people that need to be flashed and only make the flashes as long as absolutely necessary (while they're being actively shot at - you need to use the uber to block dmg). The idea is to keep your uber active as long as possible so it lasts longer than the other team's uber - that's why, while ubered, your team has to try and shoot the non ubered enemy players and force their med to flash them and waste his uber duration so you guys get a better (as in longer lasting) uber.

EDIT#2:
Some other useful crap - healing isn't just your job. It's the entire team's job to rotate the heals, and not just all come to you at the same time on 1 hp with no crit heals. Tell some of them to get a pack. Also tell them to keep track of when they've last taken dmg so they know if they have crit heals or not. That way they'll know the best time to approach you and ask for heals

The best advice is dont get overwhelmed. Sounds stupid but the more you focus on you being overwhelmed, the more you will be. Just try to relax and do your job without panicking, it will ease the situation a lot. Dont expect to do zero mistake right away, the more you play the more you'll get confident in your healings.

While in uber, try to focus it on one player, dont flash for no reason, and warn when you plan to back out so you dont bait your teammate into a fight he'll lose.

While in stalemates, only heal flanks when they come to you. If they took damage, dont wait for heals before going in the fight again and die, it's their fault, not yours. If they complain, you explain the situation. If it happens again, just demo review with them so they can see that sometimes they have to wait. And if after this they are stupid enough to keep complaining, just play with other people.

At your level, working on your positioning as medic is the most important aspect of the game you should focus your time.

It is also the easiest and best thing to observe when doing a demo review of yourself. Instead of watching who you are healing over and over, watch the bad habbits you have with your positions and learn accordingly.

Effective team healing is more about not having brain dead teammates than "healing the right person" in most cases. Rarely, if ever, should you be chasing teammates to get buffs or heal up. Having new players know how to rotate heals and stay buffed for team fights is a skill learned over time and with experience. I believe most medic mains blame themselves when thier teammates fail to know how to rotate heals. It is easy to blame the medic.

Back to the main point. Positioning. Staying alive is obviously your main goal but it is equally important to know when to commit to a fight and when to stay safe so you can bail out if things are going poorly. (team comms are important here)

Having the ability to "feel out" a team fight and make the correct decision (stay in or get out) is arguably the most important medic trait to learn. Having the correct positioning is the first step in that process so demo review and start building experience from there.

Can't contribute much but frankly, you usually (depending on the situation) shouldn't worry about buffing someone if another player is really low. Get them up a little before giving the buff. Exceptions to this would maybe be buffing the flank so they can make a distraction while the rest of you retreat.

Heal priority is not static. It changes based on what the current situation is and who's currently actually doing shit. If someone has to stop participating at all because they're so low and their class can't do much while low (scouts) then you'll probably want to get them up a bit. Not always to full, depending on the rest of your team, but getting them to about 80 health is nice.

From one low-level medic to another: feel free to inform your team that they are all very low health and need to consider backing the hell out. Your teammates are a lot less likely to be aware that they're all piss-poor health than you, so they might just be thinking, oh, I'm the only one hurt we can keep fighting. No. Tell them "we have bad heals/positioning (it's usually both when you're starting out because the second your teammates start taking damage they start shrinking back to their medic and suddenly you're all on low ground with poor health), we need to leave". You can call that you're tanking either a demo or a soldier to lay covering fire and the rest of you need to GTFO without taking damage.

You can also kind of start to see if you can recognize a pattern where healing one player is more important than another. Like say you're all low health near a choke - you probably want to have your spammy classes as healthy as possible so that they can spam out that choke and hold off the other team, giving you some breathing room, time to grab some health packs and whatever. Maybe you're backing out completely, so it's better for you, the medic, to heal the scouts so you can back up faster and also have them healthy enough to deny anyone who attempts to jump you or your teammates. Etc. I can't really give advice on this because I'm bad myself so you'd probably be better off asking a more experienced mentor.

If your teammates are making you pressured by bitching at you, seriously, either tell them to shut up or no joke go find a new team that's more mature. Med is already stressful, nobody has any right to make it any worse by trying to sway your decision for the sake of their own stats when they're probably fucking up just as much as you (by taking damage they shouldn't be). They need to learn that they are playing as a TEAM and sometimes it means giving up your own health to tank someone more useful. Like one of the things me (the demo) and my pocket are working on now is rotating aggression and heals so that we're not taking the same spam damage and that lets our medic have a clear understanding of whom he needs to tank at any given time. Ideally everyone on the team is constantly thinking about how many heals they're taking up and how to spread it out so that your team is always functioning at the best intersection between good aggression and good health.

Communication is key. Like Mallory says, keep your team mates aware of the team's health. If everyone is hurt, non essentials need to get health packs or wait. During stalemates or before a push, the flank should rotate to you for crit heals. If the flank is wasting your time coming to you without crit heals or trying to get health while you're tanking your demo tell them to gtfo. However you need o be aware of these timings as well so you are prepared to tag the players with crit heals when they come by. Smart/good players can see when a med is busy and will go get packs usually rather than complaining.