What do I do if my Xbox 360 is glitching my games and doing weird things?

If the inserter is hot, you should probably leave it for 5 - 15 minutes.

According to It Still Works:

Screen freezes can occur on the Xbox 360 for several reasons. The mostly likely reasons include problems with a game disc, corrupted installed game files, network issues and lack of airflow to the console. ... To unfreeze your Xbox 360 and help prevent future freezes, do some troubleshooting to find out the cause.

The Xbox 360's screeching sound is probably from the disc you are playing on. If the disc is old, it won't read the disc. Here is some information from Digital Innovations on how it might not read the disc:

The major contributing factor to a disc read error is a dirty optical lens (the one that your Xbox 360 laser passes through to read the disc itself). If there is dirt or dust on the laser lens, your system will eventually fail to read the game disc.

The sudden screeching must be depending on the time on how much days/hours/months in total you played Fable 3. If it is new, it is probably your old 360 itself, but you really don't need a new one, you just need to take it for repair. Look here for a reason on why it may be screeching. If the repair isn't affectable for a few minutes. You may need a new Xbox.