It sounds like your pet might be suffering from feline acne.
The current favorite topical treatment for feline acne among some veterinarians is 2% mupirocin (Bactroban Rx) ointment, used twice a day for three weeks. A published study on this treatment indicated excellent success in 60% of the cats treated, good success in 36% and one cat that developed an allergic reaction to the medication and had to be dropped from the study, making the failure rate 4%.
When feline acne does not respond to topical treatment, there are a couple of things to consider. The first one is whether or not it really is feline acne, or if it is one of the conditions that can mimic feline acne, such as ringworm, contact allergies, food allergies, yeast infections or demodectic mange.
If this is feline acne and topical treatment isn't working, the best approach is to culture one of the pustules and then choose an oral or systemic antibiotic based on the culture and sensitivity results. If this isn't successful, then it may be helpful to try isotretinoin (Accutane Rx). One of the recommended
dosage schedules for this medication is 10mg per cat once a day, which is convenient because the medication comes in a 10mg capsule. An alternative is to continue to pursue the diagnostic process and consider a skin biopsy. This can be helpful in differentiating deep acne lesions (furunculosis) from
other infectious/inflammatory conditions and that can help in determining the best treatment.
You should also evaluate the food bowls and water dishes. Some cats have allergic reactions to metal bowls and you will see lesions that look like acne but are not. If the bowls are not cleaned well, it also might be a bacterial problem.
Sometimes there aren't any pustules just black grainy/sticky stuff around the lips that scrapes off easily - sort of like blackheads gone wild. You can try cleaning it up with alcohol at home - sometimes that is enough to help if there is no other inflammation or pustules. Calendula gel is a good antimicrobial and skin healing promoter. Plastic bowls can cause a contact dermatitis also, but this sounds more like acne.
Your vet can quickly diagnose this for you and discuss your treatment options.
Let me know if you still have questions.