How could minocycline work for my acne and skin problems?

Probably quite well: This is a great antibiotic to supplement a good topical treatment like benzoyl peroxide. Never use an antibiotic as sole treatment for acne. It works by slowing down the bacteria that contribute to the disease and probably by some other mechanism as well. Best wishes for a good result in managing your illness.

Antibiotic: It's good for moderately severe acne, but never use it as sole treatment. Combine it with topical benzoyl peroxide or something similar and you'll probably get a good result.