I had perioral dermatitis and canker sores in the mouth (feels like you've sucked on lemons all tight), it was the later development of the sore in the mouth that made everything click into place. I had been using a high fluoride toothpaste prescribed by the dentist which is 5000ppm fluoride. A hypersensitivity to fluoride cause these side affects. change your toothpaste to fluoride free, don't use mouth wash and watch water, juice drinks and wine, mechanically de boned meats such as chicken nuggets. fluoride awareness sites give more details. Honestly I can not believe the difference, it was itchy, red with small bumps round my chin, started at one corner and worked across the front to the other side, and sometimes scaly, I then had the sores in the mouth but all are going / gone.
If Chapstick doesn't work, change to one that doesn't use parafin wax. Sometimes people are allergic to that, too.
I believe that rubbing petroleum jelly on the rash will help her a lot.
My daughter has something like what you described. I put it all around her mouth before bed and she wakes up looking/feeling much better. :)
Hope that helps you,
Brad