How do I stop my puppies developing aggression?

I just adopted a 4 month old bichon mix (Ceasar dog food Trademark dog) from the shelter he had kennel cough and i gave him the prescribed medication for a few days and then i kinda just stopped....well not kinda i just did. Anyway, 2 weeks later he's starting to show signs of aggression. At first I thought it was just him being playful then it started to hurt. Then I thought " well he IS teething so maybe that's it, " but here I am at 4:49 in the morning with bite marks on my hand that look and feel like I scratched myself with safety pins. The was an intentional show of aggression because he rushed me when i was comforting my other puppy. He wakes up in the middle of the night barking and when I try to approach him he backs away. I know better than to corner a frightened dog so I walk away and then he starts running around and begin scratching my ankles biting my legs. This is definitely not "puppy play" it seems he's demented or possessed. His behavior is not normal at all. I'm not saying he's possessed but im afraid it may be a my fault for not finishing his medicine schedule or maybe a side effect of his recent vaccinations.I'm going to go to the vet as soon as I can. I don't know when that'll be but I have to try and see what up in the meantime. If there's anyone out there with an answer to this problem PLEASE your reply would be greatly appreciated.