Is one chemical peel okay for my skin?

I was thinking about getting a mild chemical peel for my skin, thats not so pricey maybe like 150. I have oily skin that creates mild acne for my skin because of the over production of sebum and oil. I was wondering if one chemical peel would be enough, cause I'm not rich. lols. Right now I am getting facials every month for 90 bucks plus tip but after exactly one month my face would have little bumps again. So I was wondering perhaps I can get a chemical peel every three months or six would that show better results. Cause after all the little white head and oil is removed from my skin, my skin is super smooth.