Definitely don't do any 'pack leader' dominance nonsense. The people who
created that theory have debunked it. It will make things worse. It just sounds like a puppy who doesn't know any better and wasn't ever taught. I have an absolutely amazing dog who was trained using positive reinforcement, and a bit of my own style. I guess I'd call it 'relationship based' training more than anything.
I'm not sure you're actually dealing with TRUE aggression? It's hard to tell from your description, but it just sounds like he lacks bite inhibition and never properly learned. Puppies can be nippy, and bite, etc, and it's not them being aggressive per say ... it's more they lack the social skills they were supposed to learn as a young pup with their mother. How old was he when you got him?
Kikopup on YouTube has some awesome videos. I'd highly recommend checking them out.