After recently taking the belt off my Alternator, and then putting it back on, it squeals quite loudly when revving quickly. This never happened before. What could be the issue?

 

Any tight pulleys, weak tensioner, misalignments, or sometimes putting the used belt on backwards can cause noise.

 

Assuming this is a serp belt, probably the tensioner. By manipulating it, it may have changed the stress on the spring or pulley, or introduced some dirt into it. It's either a warning sign of the tensioner starting to go or it will go away.