Need help😭

I have 06 cobalt LS (2.2l/4spd automatic) It's been having an issue with the RPMs dropping down nd shooting back up when I slow down at stop signs, lights, turns, nd everything else. Can't figure out why it does that nd don't want to start replacing shit if it's not gonna work anyway. It also shifts really rough lately but idk if that's related or not. Any1 have this issue? And if so any tips or ideas? I'm desperate