OMG I was just going to post this same question, but my daughter is 19 months old... its just started a few nights ago and at night when she is tired or excited she has been pulling skin off my shoulder & it hurts!

She is teething atm as well.

What I have tried so far (not sure if it works yet though...):

I say "ouch" loudly and put her down straight away. If she cries or yells I tell her that it hurt Mummy & if she bites again I will put her down.

I also go into the kitchen & grab her a teething ring and let her chew on that (I keep 2 in the fridge) *usually* this stops. Last night she would stand at my feet with her arms up screaming & when I picked her up would bite me straight away and laugh, so I just put her down & ignored it but I do think its become somewhat of a game :-k I hope some of this helps!!