This puppy is just very vocal and a bit of a baby. I took him to the vet today and the gentle woman cleaned his ears. You would think he was being murdered.
LOL I have a cat that does this and one vet kept reassuring me that she was not hurting my cat. I know no one is hurting my cat - she is just whiney! The vet must have told me 20 bazillion times in that visit that she was not hurting my cat.
Every pet has their own personality. My mom's dog is very clingy and obviously dependent, mine is rough and tumble and perfectly fine with being left alone. She had a tooth fall out while she was playing and she stopped what she was doing, looked down at it, and kept right on going! Other dogs would have freaked out - just like people!
If you do not want him chewing your hands, do not let him. He is learning how to interact and play with you, so you have to set the rules and teach him how to. If he goes for your hand, tell him no, but praise him over and over when he is playing with a toy or whatever you want to consider to be proper play.
Expecting too much would be telling him once not to pee in the house and expecting him to never have an accident again.

A puppy you have to constantly demonstrate your commands and praise the off-chance that your puppy does what you are saying. For example, when teaching a puppy to 'sit', it is a lot easier if you place a treat over their head, because most puppies will automatically sit down to get a better look at it.
You do not have to be overbearing, but try not to react positively to anything that you do not want him repeating - even when he's no longer a puppy. I have a friend who thought it was so cute! when her puppy jumped on people. Well, it is not so cute! any more now that the puppy is a LARGE DOG.