Glycolic Peels in Between Laser Hair Removal Treatments?

I have been getting pimples (including 3-4 deep ones) and whiteheads on my cheeks and neck, at the time when my hair is shedding. Almost all the dried pimples and whiteheads that I squeezed out had a hair trapped in it. My skin look bad now and I am thinking of using a 15% Glycolic peel to help resurface my dead skin. I have used 10% Glycolic peel which worked wonders for me but I want to know if I could use a peels in between Laser hair removal. My sessions are spaced at 5 week intervals.