I have had experience with chemotherapy burns through my sister. Unfortunately the experience was not very good. If you have the experience that Melanie Haiken indicates "but it's possible for a severe burn and ulceration to develop" you may have a bigger problem. My sister contracted lymphatic leukemia over 30 years ago. New methods of treating it with powerful new drugs just started. Needless to say the hospital and the caring physicians saved her life.
Unfortunately during administration of the drugs a needle was improperly placed and a severe burn resulted. It left a scar on her lower arm at the point of insertion about 3 inches long and 2 inches wide. It looked like a rectangle missing one long side. Many years later a large cyst developed on her arm at the site of the scar. No doctor has been willing to do anything about it due to the risk of infection from surgery. Once in a while she will have calcium drained from the cyst.
The skin around the site is thin and tender and it has recently developed an infection. A doctor has recently told her to soak it and take antibiotics. So we are hoping the infection will go away. Based on her doctor's advice we may need to see a skilled plastic surgeon.
My point in writing this is to inform you that burns from chemotherapy can be permanent and they are difficult to deal with. There don't seem to be specialists in this area. Until hospitals can come up with dedicated units for these serious burns you are pretty much on your own.
My immediate suggestion would be to take Ms Haiken's advice regarding talking to your oncologist. And I would also suggest getting in touch with a skilled plastic surgeon who might be able to do something early on. But continually keep your oncologist up to date on any recommendation of treatment and lean on him or her for another opinion especially if a recommendation is surgery. The area around the site is highly prone to infection so any decision regarding surgery must be well considered.
While this unfortunate event occurred please understand that I will be eternally grateful to the hospital that saved her life. I would never have believed that my sister would be able to be a part of my life for these last 30 years.