H.W.
Babies get diarrhea when teething because they are swallowing lots of saliva and drool,which is acidic. This causes a diaper rash.
At diaper changes, here are some things you can do to alleviate the burning for her:
Rinse out the wipes in warm water, twice, to remove the soap.
When bathing, do not use soap. Just warm water. Soap is an irritant to broken skin.
Change diapers, wet or soiled, more often. Do not leave a wet or dirty diaper on any longer than absolutely necessary.
When changing a diaper, consider having her 'air her bum'; if she doesn't get upset at the sound, you can use a hairdryer on 'cool' to aim air at her bum to dry it completely. Be sure to keep your hand on her upper thigh and to check the skin to ensure it doesn't get too hot while using the hairdryer, so you don't burn her. Keep the air moving around the area, not just in one place.
Use a good cream like Weleda calendula cream. If you don't have that, a moisture barrier like desitin or A&D ointment can help. DO NOT use vaseline.
The rinsing of the wipes, thorough drying and frequent diapers changes are very important. If it begins to bleed and doesn't improve after a couple days of being consistent with those tips, do consider taking her to the pediatrician and ask if she might have strep. Some kids get 'strep butt' which is a strep infection on their bottoms. This is usually cleared up with topical antibiotics, if I remember correctly.