It sounds as though it could be one of a couple of different things; either a feather cyst, or a tumour. I am familiar with tumours as my budgie Skyla had developed one under her wing. It kept growing so we decided to have her wing amputated. Yes it sounds drastic, but she lived a happy life with only one wing until she developed a second tumour near her tail feathers which eventually decreased her quality of life significantly.
Please don't euthanize your budgie until you notice that the quality of life is deteriorating. I was faced with possibly euthanizing Skyla and just didn't know if it was time. I figured that when she was having more bad days than good ones, then it was time. I never had to make that choice as she unfortunately passed away on the way home from a vet visit just before Christmas.
Anyway, I am hoping it is simply a feather cyst. Regardless of what it is, if she picks at it, you will probably want to keep her from doing so as much as you can. My budgie Skyla would pick at her tumour near her tail and it would bleed quite a bit so we had a collar put on her (it wasn't a cone like the ones you see on a dog for example, but rather a clear plastic thing that snaps on around their neck). It took her a few days to get used to it, but then she didn't even notice it was there all that much.
Please let us know how your little budgie is doing.
Proud owner of two budgies: Aries, Gracie
Remembering Apollo (my first ever budgie), Skyla (my one-winged wonder) and Kiwi (my "little big boy")