Kona has had feline chin acne, too. Some looked like little blackheads, and some looked like your pictures. Her vet said hot compresses would help (she didn't care for that much) and to make sure she didn't scratch them and make them worse. They healed well, and she hasn't had an outbreak in a long time.

He explained that sometimes this is caused by the scent glands in her chin producing too much oil, which clogs the pores.

Good luck at the vet, Pixel. I hope your chin gets well soon!