Your description is compatible with both adult acne and perioral dermatitis. Either one produces pimples around the mouth. Cause is unknown. Cortiosne is unhelpful or worse and should be avoided. Toothpastes and similar products don't seem to matter in most cases.
I think a topical (
externalExternal incontinence devices) antibiotic is more likely to be helpful for intermittent use. If your doctor considers this perioral dermatitis, an occasioanl course of dixycycline or similar anr=tibiotic may be useful. Whether it's one diagnosis or the other, you needn't be concerned about a lifetime of rashes. Both peter out over time. Maybe a couple of more years.
Best.
Dr. Rockoff