I have suffered from this for years on and off and then during pregnancy it became completely horrendous, covering right round my mouth, chin and up around my nose. I previously had (temporary) success with antibiotics in the past but didn't want to take anything during pregnancy so went looking for a natural treatment.
Having tried a whole host of things I found the best solution to be Aveeno moisturing cream and Aloe Vera gel and strictly (and I mean strictly!) no makeup in the vicinity of the offending area.
The aveeno works straight away, stopping the dryness and peeling and calming the redness of the skin. The aloe Vera takes a little longer to work but eventually it will get rid of the pimples and weeping rash and help to heal the skin.
Apply both twice a day (morning and night). Keep skin clean and don't pick it. The only other product I use is Clinique mild facial wash as it seems to clean deeply but doesn't irritate or dry the skin.
Generally I have found less is more with perioral dermatitus, i.e. Don't slather on lots of product but use as little as possible and be patient. Once the skin starts to improve try reducing the application to just in the morning if possible as it gives your skin a chance to get back to 'normal'.
My breakouts were caused by using foundation so even now my skin has healed I never use foundation around my mouth. Having a job where I need to look 'presentable' this can be a bit problematic so I do sometimes resort to using a tiny bit of no. 7 liquid concealer stick in local areas which doesn't seem to cause a breakout providing its well washed off at the end of the day. Perhaps over cautiously I also replace the stick monthly so as to avoid any potential bacteria building up which could cause another breakout.
Anyway....I truly hope the above is of help. And good luck, it really does suck and I have every sympathy with you!