Is my baby teething?

He’s 3 months old. He drools constantly. Is always putting his hands in his mouth. But this past week he has been insisting on chewing on my fingers and he chews hard. He also just started biting down on my nipples when feeding. No idea if this is a developmental thing or if he is teething. His gums don’t look red or any different than before. So it’s hard for me to tell! Today he was extremely cranky and was only consolable briefly if I let him gnaw on my fingers.