It is impossible to know what type of chemical peel you had based on your description. However, you doctor should have fully described to you what to expect on a day by day basis so you don't need to sit around and wonder.
It is my practice to see my patients quite frequently after a peel so they stay out of trouble.
From the description of your peel, it is unlikely that you were peeled with anything stronger than 35% tricholoacetic acid (still considered a superficial peel). Even this peels hurts enough that one benefits from drugs and local anesthesia before the actual procedure.
I am concerned that you have not been properly instructed in the care of this fragile peeled skin. The skin should not be allowed to dry out. This makes the skin uncomfortable and can unnecessarily prolong healing. You should keep the peeled skin hydrated by applying a thickish layer of Vaseline (go to the drug store and get a new tub) to the skin. This will rapidly melt off the skin and needs to be constantly reapplied. I also find that having my patient shower 4-6 times a day help to hydrate the shinny peeled skin which will peel off the face in sheets in about 4 to 5 days after the peel. As this happens, avoid the temptation to tug off the peeling skin as you can tear and damage the underlying healing skin. By day 5 or 6, the underlying skin should be intact although dry. Within one or two days, the skin will be ready for moisturizer and will also hold make up.
Good luck with this and do let your doctor's office know that somewhere you must have misplaced the instructions that talk about what to expect following the peel and how to take care of the healing skin.