Chemical peel on hands for $75.00. Could only wear gloves for three days.

Without knowing exactly what type and what strength of peel you received, it is hard to know what the post-peel protocol should have been.  However, as long as you are using a high quality, physical block sunscreen and reapplying it frequently and you are using a good moisturizer, you should be fine.  I would recommend following up with your skin care specialist if you have concerns.