My little girl has had something similar a few times. The first time was right after her second booster shot. My old vet said they were spider bites. They looked like pimples to me? Since then, I got a new vet that is holistic. She is awesome! Finally someone that doesn't look at me like I am killing my puppy for feeding raw!
She said they are called puppy pustules. They get them after the shot because the vaccine tanks their immune system. Their body can keep the normal bacteria that is on the skin in check. When their immune system is down, they can't keep a handle on it and it goes out of control.
We did antibiotics the first time, and they cleared in about a week. The second time, we went with a different antibiotic, and they cleared much faster. The third time, I just kept an eye on them, and eventually her body took care of it. I would put a little Neosporin on them every day.
She will get one or two now and again, but her immune system just takes care of it.