You can call a few dermatologists' offices, say that you're interested in a consultation but haven't got insurance, and ask how much that will cost. Usually, secretaries will be sympathetic and will happily let you know the rate ahead of time. Additionally, you should ask if there is a discount for paying in cash or by check - very often, doctors will charge uninsured patients less than those with insurance, because insurance companies have private deals with the doctors that mean that they already pay less than the normal rate, and because they have nothing to lose by charging insurance companies more for certain work, but they might lose you as a customer if they try to charge YOU too much. (For example, if a doctor is in the Blue Cross Blue Shield network, then even though her normal rate might be $200 an hour, the insurance company might only compensate $170 an hour for normal work. In exchange, more Blue Cross Blue Shield plan members might use that particular doctor. Often, doctors will be willing to give you that same lower rate if you ask, so that you'll only have to pay $170, because the whole reason they charge so much is to try to get that basic amount out of the insurance companies.)
If you find a dermatologist whose price is right, then go right in. You should be unashamed to tell the doctor that you don't have insurance, so you are hoping for a treatment that requires a minimum number of visits or a minimum cost to fix. I think it probably would make sense to try to budget at least a follow-up doctor visit, as well as the cost of some kind of medication, but beyond that, you should be clear with the doctor that you are on a budget.
In NYC, sometimes your best bet cost-wise will be quite far across town. If things are too expensive near where you live, try calling a dermatologist in another borough. You can also try medical practices that are associated with various hospitals in town.