1. How big is your enclosure? How many fans?
   
2. What are your power settings/What is your power plan? If its "High Performance" or "Maximum Performance" your CPU will go balls to the wall at any load you give it. Use Resource Monitor to find what's causing your CPU to spike.
   
3. Is the room the computer is in air conditioned?

You might be able to get away with just an aftermarket CPU cooler or a more conservative power plan but some Haswells tend to run hot.

I'm using an s340 with plenty of airflow. 3 fans, 1 in the back and 1 in the top blowing air out and 1 in the front blowing cool air in. My power plan is currently at high performance and though the place i'm in can be a little warm it definitely wouldn't cause this. Like I said 3 days ago everything was perfect. I haven't changed anything since then

That's a pretty big enclosure, so that's good, assuming it isn't in a desk cabinet or something. Temperature fluctuations in the area the computer is in will have an effect on heat, but if it's below 95f you should be good. Assuming you didn't do anything on the 2nd CPU cooler install like not tighten the retention screws all the way, you would probably be good with an aftermarket cooler.

I think you misunderstood me. It hit 95c not Fahrenheit. Temperatures seem to have gotten way worst. Not only is it fluctuating like that, but when things were working perfect my cpu would be like 60c when playing tf2. Now its like 70-78c

I mean 95f room temperature. If a room with a computer raises in temperature, the temp for the computer raises as well. If I turn my air conditioning off my temps raise about 15c. Outside of the stock CPU cooler not being able to handle the combination of sucking, external heat and a hot Haswell, I can't think of anything else that would cause this.

Intel's stock coolers are garbage. Check the plastic clips again. If you added thermal paste did you remember to remove the thermal paste that was already on the cooler? If all else fails get some cheap aftermarket cooler with heatpipes.

I did NOT remove the thermal paste that was already there. Should I clean both the cpu and heat sink with rubbing alcohol?

Yes, strip everything off down to the bare metal on the cooler and try again.

and put a small dot of thermal paste on the CPU once you have both the CPU and cooler cleaned. Be certain not to put too much on.

Vid for reference https://www.youtube.com/watch?v=rjF5jabXRCY

Yeah I know. People often say a size of a pea/large grain of rice in the middle is the perfect amount

Could someone move this to hardware? Do mods even exist here?

I'm not sure if I got all of this so correct me if I'm wrong.
Your CPU sits at 30°C idle? That's normal.
When the there's load on the CPU the temperature spikes? That's normal aswell.
Higher load -> higher temperature, even while browsing there will be load spikes for example scrolling is basically no load, whereas to load a website the CPU will go balls to the wall so it's finished within a second and then clock down again. The heat produced will heat up the CPU almost instantaneously and slowly dissipate again. Even with a constant load the temps will spike at first and then go down a bit again because the cooler needs a few seconds to rev up for three reasons.
1. There's mechanical aspect. Doubling the rpm instantly just isn't a good idea.
2. It only reacts to the temps, it can't them so it'll always lag behind.
3. The reaction is actually delayed on purpose. Imagine the temps spiking from 30°C to 50°C every few seconds with the cooler reacting instantly. quiet -> jet engine -> quiet -> jet engine. Very calming and enjoyable.

Now those 60°C were indeed fine. 97°C aren't. If you didn't remove the old thermal paste then that's your problem.
Regarding thermal paste less is indeed more. You want just enough to fill the irregularities (otherwise filled with air, which is very good at isolating) in both the IHS' and coolers' metal surface to get full contact across the whole surface, but not any more than that. If there's so much thermal paste that the heat has to go through it even where the metals would be touching if there was less, it'll degrade performance. This is what you're seeing right now.

With the pea method if after you've secured the cooler you can just barely see the TP in the middle of the sides, but not across the full length, not at the edges, then you've done it right. A bit less is fine too but you obviously can't see anything in that case so you might have to remove the cooler and check if you're not sure and then start over again.

Which thermal paste are you going to use?

Shin- etsu microsi paste

Well I cleaned the existing thermal paste and reapplied it and....Everything is still spiking and very hot. Ran it through the Firestrike benchmark and it hit 100c during the physics test....Everything was fine 3 days ago and this happens....Did I get a defective cpu?