I had a Glycolic peel, but my skin didn't peel.. why is this?

It's a lighter chemical peel and probably you need a stronger one. I wouldn't reccommend you doing it yourself but going to see a doctor. If it is a TCA peel and you do it yourself you can really damage your skin. Don't use over 10% glycolic at home. At home I used Jan Marini Bioglycolic acid cleanser and my skin always peeled. Google Jan Marini products. Alot of people like it.