M.B.
As far as I recall, BFing should not make teething worse. Also, it is not at all unusual for a baby not to take a bottle when mom is around - they're smart and as welling as providing nutrition, BFing provides the ultimate in emotional comfort and if he is in pain, BFing should actually help him feel better.
It's possible that the Tylenol is bothering his tummy and lying in the nursing position could make the tummy feel worse. You might try just rubbing Motrin directly on his teeth. That can be much more effective than expecting the tummy to process and then have it get to his teeth - i.e., if you're using the dropper, it might be going straight down his throat When I have severe tooth pain, I actually do that with the children's motrin.