Finally painted over that hideous 1970s paneling in my hallway and it took 3 coats but the difference is night and day | Diy And Home - Chatter Central
Primer is the way to go for sure... but honestly even with 3 coats it might peel later if you didn't use a good bonding primer on that old paneling. The gloss on that stuff is super slick and paint just sits on top without something to grab onto. Hopefully you used at least a coat of Kilz or Zinsser before the actual paint. If not, just keep an eye on it and dont touch the walls too much for a while.