I have never had an overheating issue with my computer ever, but I think it might be overheated. It's shut itself off twice when I heard the fan was really loud and the casing was really hot. I let it cool off for a bit and it still shut itself down after 30 minutes. I turned it on again 2-3 hours later and it's now making a really weird buzzing noise.

Is there anything I can do? Can I buy a better fan or something?

First thing would be to open the case and take a look inside. Is it dusty? Are all of the fans spinning?

It was a bit dusty and I barely cleaned it. Should I get rid of all the dust?

oh that's weird. My laptop does that too. What I have to do is be careful I'm not like "overwelming my computer". Like say you got your music going on the laptop, then have ten other things running at the same time. That's what usually kills my laptop. And another thing is to just check once in a while if its getting too hot as you use it.

Define "buzzing" sound. Electrical buzzing? mechanical buzzing? Grinding?

What are the temperatures you are getting? (use a program like http://www.almico.com/sfdownload.php)