I don't know how long its been there, but as always, the best thing to do is tell your doctor. Call to see if they, MO, RO or ENT, can move you to an earlier appointment, otherwise, wait to show the dermatologist, and it may even dissappear by then. It's common to have swelling under the chin from lymphatic fluid build-up due to radiation and or surgery, mine was the size of a golf ball, also called a turkey neck. I showed my RO, who discounted it as being cancer, so I just ignored it, never showed on any scans, and took a year to somewhat disappear. There is also the submandibular salivary gland tat could be enlarged or duct blocked. It's difficult to tell by the feel of a lymph if it's is cancerous or not, except for a very skilled doctor, and could be moveable, especially when small or fixed, firm, when it attaches to structures, but not always. It's more the shape, tear drop, center thickness they rely on, I believe, and out of my scope.

You mention skin breakdown, and could be an infection also, such as an abcess, cellulitis, so monitor that for fever, increase in size, redness, spider veins, and any infection can get serous rather quickly. I had an abcess surgically removed from the side of my chin, and with a compromised immune system you are more susceptible to infection, which can go systemic if not treated properly.

Good luck with everything.