I had what i thought was an ingrown hair on my private area, but it popped open the other day and now it looks like an ulcer. i am not sexually active, so what could it be?

Herpes I/II is very contagious, and oral contact with a carrier can be transmitted to the genital area without sexual contact, from the mouth via hand/finger contact with saliva and incidental touching of the genital area with bath toilet. Ask your gyn provider to obtain IgG/IgM antibodies tests for Herpes I/II. If negative, see a dermatologist for diagnosis resolution.

This is most likely a ruptured or infected cyst. I would recommend you see your primary care physician.