[Troubleshooting] Removed my heatsink, reinstalled it, now CPU temp shows 99 degrees Celsius when launching applications?

Kind of a long title, but it pretty much sums it up.

I removed my stock heatsink from my motherboard in order to install a new one I got over Christmas break.

But when I saw that the new heatsink required me to unscrew my motherboard, I decided to do it another day, and placed my old heatsink back in.

I noticed the thermal paste was really dark and it looked kind of hardened when I put the heatsink back in.

Now, my cpu idles at around 55 degrees celsius (I can't remember what it was before) and whenever I launch a game from steam, it shoots up to around 75, then goes up to 99.

Did I do something wrong when I took my heatsink out? Are you supposed to replace the thermal paste after a while? (I've had my computer for about 6 months and haven't replaced the paste since)

I'm getting the temperature from Speedfan, CoreTemp, my motherboard's tuning utility, and my BIOS, they all say the same thing.

I also did a virus scan, and nothing showed up, but I'm using my university's antivirus and it's kind of bad, so maybe it missed something?

Anyways, TL;DR: Took out heatsink, put it back in, CPU gets really hot when I launch programs. Why?