The burning the skin part makes me think food allergy. You can develop food allergies and sensitivities at any time- even to something you have eaten for YEARS. A lot of times stress will trigger the reaction.
Intestinal distress makes me first think of gluten sensitivity. Does she eat any oatmeal, wheat, or rice cereal? Even the rice may have some gluten unless it states specifically that it is gluten-free. The Aveeno could be making it worse rather than better.
Calendula (try Weleda brand or look in the homeopathic section of your drugstore or health food store) helps calm skin after a bad abrasion or burn, and will work wonders. Most of the butt-paste and vaseline type ointments are going to have perfumes, chemicals and a petroleum base, which will only make things worse if she is sensitive. I would definitely go the herbal route.
If you are breast-feeding, cut wheat and dairy from your diet for a week and see if that helps. You may have to cut them indefinitely if she is sensitive. You can also use breastmilk directly on her diaper area and let it air if possible. Breastmilk is very healing because it has antibacterial properties.
My youngest daughter had a dairy sensitivity and it would cause very strange poops. She would also get a burn-type rash from me eating spinach, pumpkin, sweet potato, and anything very acidic- like too many tomatoes or oranges.
I hope this helps and she (and you!) find some relief! It sounds like you need a new pediatrician if they aren't concerned about a 7 month old's terrible diarrhea. She is definitely young enough for this to be a real emergency. Please keep a check on her for lethargy, a sunken fontanel (soft spot) and glassy eyes- all signs of dehydration. If you are in doubt or feel that something is just not right, PLEASE take her to the ER for fluids or an evaluation.