Why is my system overheating?

I've had the system for a few years and until last week it has never been cleaned before. The fan was loud but not to bad. I never had any issue out of it. Last week I had disassembled it and gave it a very good cleaning. The system was packed with dust. Very dirty. I used canned air to get dust out of small spaces and I cleaned the fan very well. I also replaced the thermal paste with Noctua NT-H1 Pro-Grade. I reassembled it and made sure everything was connected and placed properly. It started no problem. I could watch movies on apps and download games. Once I started a game disc the fan got really loud and shut off and I heard a few beeps. It did that 3 times. I tried a different game and it didn't turn off but the system literally sounding like a jet about to take off. Now I can play games but the fan is still very very loud and it doesn't sound good during gameplay. When I look up the symptoms all I get is it could be dust (No dust at all and replaced thermal paste) or the fan doesn't work (fan is definitely blowing out air) does anyone have an Idea?