Hi, thanks for using Petco Pet Education Center, formerly Petcoach! Poor baby!
I would have Billy dewormed and a stool checked for parasites. At 7-8 weeks you need to start his puppy vaccines (DHPP). At this time he should eat canned puppy food and you can add puppy formula for a week or 2. I do not think he needs to be bottle fed at 4 weeks.