You can buy teething toys and see if it helps with the biting of the hands
I’m not sure if that’s the thing isn’t she too small for teething
My daughter was also born at 31 weeks and is 4 month now. Shes been drooling and putting her hands in her mouth for a few weeks now. Google mentions this is normal discovery for her age and could also be teething which can start at 3 months.
Her teeth may be starting to come in (teething)