Certainly, it is possible to have a localized skin yeast infection, but I'd also consider other things. Do you or your partner have any history of herpes (or even cold sores, if you ever have oral sex?) Please forgive my intrusion, but just trying to think of anything possible.
An inflamed or infected sebaceous (skin oil) gland can also become inflamed anywhere on the female genital area, and this can happen to anyone at any time.
Rarely, abnormalities of the skin of the vulva
(vulvar hyperplasia or other skin or precancerous abnormalities) can cause localized burning and itching.
If you are comfortable doing this, it may be worth using a hand mirror to look at the area, to see if you can see any other changes. Pay special attention to any areas that look like sores, paper cuts, or "pimples". It would be harmless to try soaking in a tub of warm water for the soothing effects, and if it persists, you will probably be best off seeing someone who can examine the area for you.
My best of luck to you in feeling better, and I hope this has been helpful.