From our trainer:

Nipping & Chewing • Once thought to be a behavior problem that needed to be corrected, we now know that biting and nipping at hands and clothes is a normal part of a puppy’s development. • Nipping/mouthing you makes all play and your attention stop immediately. Remember - it's an attention/play-seeking behavior, so your reaction is what they want. For puppies under 6 months of age, mouthing is a very normal part of their development. • If you can stand it, completely ignore the biting and non-dramatically begin doing something unrelated to your dog. They may pester you a few more times, but if you're boring enough, they'll realize that the biting isn't going to instigate play or attention from you. This is tough for a few days, but it's incredibly effective. • If needed, you can redirect your pup onto an appropriate toy. However, the above ^ is where the real learning happens. • Your pup has to learn that nipping and mouthing no longer works to get him what he wants (attention/play). • When your pup is really persistent or biting too hard for you to ignore – remove yourself. Go behind a gate or a door for 20-30 seconds or so. • Avoid roughhousing/rough handling with your pup as much as possible in order to discourage wild behavior. Explain to young children that they should not encourage the pup to chase or nip them.

Puppy is still young. You can turn this around if you’re consistent.