Warm compressing the chin with a warm washcloth will help open pores. Try to express any pustules that you can. Then scrub the chin with a gentle cleanser like Phisoderm. Then warm compress again. Try to do this twice a day for the first few days, then once a day thereafter until it is healed.
If the chin is very bad and isn't improving, you may have to go ahead and get antibiotics from your vet. Some of those pustules can be deep and get infected, which is irritating and painful, as you already know from experience. And systemic antibiotics are sometimes required to take care of the issue from the inside-out.
To prevent future break-outs, make sure you are using stainless steel, ceramic, or glass bowls - NOT plastic. Plastic is too porous and holds bacteria which your dogs chin rubs against during eating, depositing food oil, residue and bacteria onto the chin. Even with the other bowls, make sure you are washing them with mild soap and water every day. Scrub the chin with a warm washcloth periodically (every few days) to remove any oil/debris that may be lingering there.
Good luck!
