Teething already? 5 weeks old

Kiki • 🌈🌈🌈

My baby has not been able to sleep deeply for the past couple of days (wakes up during naps often) and she has been drooling lots (this morning her onesie was soaked). She is only 5 weeks and I am concerned that she is teething already? I can see her teeth through her gums and she seems to want to bite everything that is put in her mouth (her hand, my finger, my nipple while nursing). I know she isn't hungry because this even happens when she has been fed. Any ideas?