Is is possible to have a yeast infection only on the skin?

I know this is TMI, and I normally wouldn't share. But I have no evidence of an actual infection (I've checked), and It's going to take a few days to take off to go to the doctor.

I have a white discharge in the folds of my clitoral hood. My clit is red and itches.

However, the rest of my area is completely ok. No irritation of the lamia or vagina. No discharge. No odor. No pain or problems urinating. This is strictly my clit.

**Note**This did happen after taking a shower with a scented soap, trying to make sure I got clean between my legs. I did not use soap in my vagina, but possibly my clit. This soap dried my entire body out and I will be changing it.