Could my baby be teething?

Ha

Does it sound like my baby is teething? He will be 6 weeks on Thursday. He has been crying like crazy, will only sleep on my chest (in the dockatot normally he will sleep fine now he hates it), always wants to bite something (prefers my finger or his hands), and drools all over himself... No fever but he has a bit of diarrhea. I noticed his gums look swollen and I see indents (like two lines) where his bottom two teeth should be. None have come through though. This is so not normal behavior for him and I’m not sure if he is teething or not.