I would say you need to scrape and sand off as much as you can and then seal it with either bin or Kilz primer before trying again with a finish coat. I had wainscoting that was probably painted with oil based paint and then painted over with latex without priming by the PO and it peeled off gradually for over a period of years. I ended up scraping off anything that was loose and sealing it as above and repainting with latex. I hope you didn’t paint a lot of it.

If you use nail polish remover, and the paint comes off it is latex, so I would see what the paint underneath is. Latex should be fine over oil based paint, the reverse will not work. Are you using a high quality paint?

Latex over oil - no. Only a few will bond and adhere sufficiently without a primer

Oil over latex - Yes, all day long it will be okay

Sand , fill the scraped areas if you like, bonding primer (i don't use oils anymore as it is 2018 and there are several water based primers/sealants that will be just fine and hold up), 2 top coats latex wall paint of your choice.