It doesn't sound like aggression to me. Puppies are exuberant, and do not have appropriate boundaries, which they need to develop as they mature. Since puppies play with each other by biting they don't understand that this is not appropriate with people.
I recommend that you make sure there are lots of good soft stuffed toys available, and watch your dog closely when he is zooming. Hold a toy in your hand and if he starts to jump towards your arm, stuff the toy into his mouth instead. Play tug or fetch with him. Distract him and redirect his attention to the toys instead of to your body. If you do this consistently you can avoid getting his mouth on your arm. If he manages to grab you unawares, say "ouch!" very loudly, and then leave the room, shutting the door behind you. Stay away for five minutes, then return. Repeat as needed. Your puppy wants your companionship; he will learn that he can play with you with toys, but the moment his mouth connects with your body all the fun stops, and you go away.
Be patient and 100% consistent with this. It will take a little time, because he is a puppy, but he will learn.