My son did this and always had a huge, gross looking bump on his thumb, but your daughter's situation is much worse even than his. I think you have to be very careful what you put on her thumb because of the risk of ingesting it. For example, Vaseline is a petroleum byproduct - it's not meant to be eaten! The stinging when you apply it is also a problem - for her and it can be a signal that what you're using is not a great idea to get into the blood stream. I would definitely talk to the pediatrician if there is any chance that she will suck her thumb with anything on it.
You could work at healing from within too, with a really outstanding nutritional product. Reliv's "Now for Kids" gets into the individual cells very quickly and boosts the immune system. This is great overall, but it can help with the skin healing. It helps with rashes and eczema too so the skin, as your largest organ, is definitely getting the benefit. There are no warning labels on Reliv so it's all food - you can give her as much as you want. It comes in vanilla and chocolate. I'm happy to share more info.
Good luck!