Nipping to Chewie
Here's a trick that worked for my cousin's pup Nipper, from his puppy class trainer.
The technique uses butter and a toy as a scent attractor and as a redirect distraction from the people nipping.
Put a tad bit of butter on a toy and hold it in one hand. When the pup nips the empty hand or a foot say, "Ouch, No." Offer the hand with the toy, and say "Chewie.'' The scent of butter will attract the pup to the toy, and the right toy will distract him from chewing on you more often than not.
It took about a 10 days of this, but Nipper's bad habit improved greatly and he learned to love his tiny Kong toy.
Those sharp puppy teeth really hurt. I hope the nipping ends soon. Good luck.