2006 Kia Optima Power Steering and AC compressor troubld

I have a question about a 2006 Kia Optima. The AC would squeal when you turned it on. It also had a leak in the power steering pump that was driven with for over a year. I replaced the power steering pump and everything ran fine for a day or two and then the belt that had a chip in it to start with, shredded. Replaced the belt and immediately the AC compressor went out. When you turned it on it wouldnt blow air but the RPMs were fluxing from 1-2k, What could have caused that? Maybe the belt was too tight? At one point during changing the pump I got distracted bc I was helping someone else on another project and forgot to put the belt on before I started it to bleed the fluid. Could that have fried the compressor? Just curious what it could have been r if it was just going bad to start with bc of the squeal? Any insight would be appreciated.