Mollie:
I sympathize!!! I suspect that is your urethra. It runs down along the anterior wall of your lower vagina and when estrogen levels decrease, the last couple of centimeters before the opening(where you urinate) can sort of sink down and show up as a mucus covered ball at the opening of your vagina, showing up right in the middle when you look in the mirror. It should be attached at the top or front part of your vagina/vulva. Don't worry, it is all covered by vaginal mucosa which is why there is mucus. You are able to see it so well because maybe? your vulvar folds are flattened and thinned also so you are more "open"? It feels like thrush because that is what vaginal dryness, then atrophy feels like and if it gets worse it burns constantly. If soap gets on it it burns, if urine gets on it it burns. When not burning it feels like a golf ball sitting at the entrance with irritation. DOES THIS SOUND LIKE WHAT YOU ARE DEALING WITH?

It can get better in a week or a day and then come back. Even when not too bothersome, you are constantly AWARE of your bits.
Sometimes this happens before major physical changes show....it did with me. Part of the irritation may be from your bladder/urethra as the mucosa can thin there in menopause also. It is hard to tell the difference where the pain is coming from sometimes...bladder/urethra or vagina (down low). All the docs said everything looked normal, but I still felt the nerve pain and it burned. I was tested for all kinds of infections of the bladder and vagina at least 3 times and nothing showed. I tried many things to stop the weird sensations, irritation and then burning for several years. Local vaginal estrogen made me worse, because the doctors gave me creams and I was allergic to the fillers in the creams. Systemic HRT was finally the answer for me.
You might ask (OR DEMAND) to be allowed to try some local vaginal estrogen to see if it helps. In the mean time, you could consider to try a 1/2 teaspoon of baking soda in a glass of warm water and see if the burning goes away in about an hour or so. Try going without knickers at home and spray off with water after urinating instead of wiping. Ibuprofen can help too.
Good Luck!
Take CKLD's advice and ask them if it could be vaginal atrophy and ask for some local estrogen.
Please let us know how you get on, OK?
Andius