I agree, not stuck shed at all, he may have been shedding when it first appeared, but that's just a coincidence. You need to tell your brother that #1 stuck shed doesn't start out small and grow larger, because stuck shed is dead skin, it can't grow at all, and #2 it' been growing for 3 weeks, so it's only getting worse and worse, and a vet visit immediately will cost a lot less, the longer he waits to take him to a certified Reptile vet that knows about Beardies the more serious the condition will get and the more money it's going to cost him.
I'm voting for a fungal infection or an abscess that may have developed from a cricket or other feeder insect bite. Either way it needs to be either drained if it's an abscess, have a skin scraping test done if it's a fungus, or biopsied and removed if it's fibrous and most likely will need antibiotics and possibly pain meds depending on what they do.
Please try to get him to a good, experienced reptile vet asap before it gets any larger, he's just a young guy to begin with and not very large, so it's a pretty good size growth in relation to his body.
Thanks so much for caring and wanting to get this taken care of properly.