I was at a flea market, and saw a copy of Crysis Special Edition. For the price, I figured it'd be worth it to try and see if it worked. It did, but there's just a bit of damage on the edge of the disc. If you run your finger along the edge, you can feel it, and looking at it from the top, you can see it's a little... frayed looking? White, not clear. When I stick it in the drive, it takes a long time to read and makes this horrible sound that certainly doesn't sound good for the computer. Is there any way to fix something like this?

Sorry, no solution to this...

ASAP use Alcohol 52% to create an image (set MINIMUM possible reading speed) and run game from it.
Avoid to spin disc to high speed - it can break into pieces. Had similar experience - new drive was needed :-(

Eeh, that sounds bad.

I was imaging damaged CD with cartoons ...I set speed to x2/x4 - the process went fine, but when I closed imaging application - CD driver spinned drive to maximum and kaboom...

So, what you're saying is I should use my dad's computer to do this job, rather than my own?

That depends entirely on whether your dad owns a gun.

Or who is paying for new drive :-P