I have to agree with the other post regarding trying Motrin instead of Tylenol (6-8 hours versus 4-6), and I would also try teething gel. It's topical and you just rub it onto his sore areas. For my daughter, this allows her to sleep better at night, and also allows her to try to eat a meal (she's working on her 2 year molars).
As far as the chewing on his fingers, it's soothing for him. If you put Aquaphor on his face around his mouth (after a bath at night time) it may help with chapped skin from all the drooling.
It's a tough time, but it will subside. Hang in there - both of you! Give it a try. If you're still not sure about what to do, always consult your pediatrician. They usually have good ideas.