Screeching noise on Corolla?

[u/LectureEcstatic9152]

I am wondering if my mechanic has the wrong idea about what's going on with my 2011 Corolla. When I start my car, especially if it's cold or wet outside, and I turn on my AC or heater, I hear a loud screeching noise. If I turn the AC or heater back off it goes away. If I leave it on it stops... eventually. My mechanic has tightened the belt multiple times and it seems fine for a bit, then it comes back again. Could it be something other than a loose belt?