I'm allergic to both salacylic acid and benzoyl peroxide so is there any acne creams that i can purchase at a drugstore without those two ingredients?

Irritation: These effects are irritant and not allergic ones. There are other options which may work for you but will likely require a prescription from a doctor.

Better see your doctor: acne requires at times prescription medications and regular follow up, till this stage is over , as Dr Chiu said you might not be allergic to benzyl peroxide, may be just irritation, good luck