I have a dry flaky peeling itchy patch of skin on my vagina after I cut myself while shaving. Its been there for a while now. I have not had sex. What should I do?

Epidermis. Shaving can irritate the epidermis and cause it to hypertrophy (skin cells pile up instead of sloughing off like normal skin does). This can cause a dry patch. Use a topical cream such as aquaphor to decrease the dryness in that area. If that doesn't work, see your doctor as it may be caused by other problems.
Infection. If the area is not getting better or is spreading, it might be possible that you have impetigo. I would have it checked by your doctor.
See a GYN MD. The area may still be healing or not. See a gyn md to be certain.