When we frist noticed bumps on Camis chin I took her to the vet. Same diagnosis, acne. It was a mild case and antibiotics were suggested by I opted to not use them.
I starting taking a small pin and actually popping the pimples and squeezing them (I know gross), and then applying peroxide and then neosporin. After they cleared up I started cleaning her face off after all of her meals. She hasn't had any since. Also I have heard that plastic food bowls can add to the problem.