Allergic to BP, face so sensitive it cannot tolerate any topicals even gentle moisturizer. Wash face 2x day. What else can you suggest 4 my acne? Time?

See a dermatologist. Maybe you will improve with doxycycline 20, 50, or 100mg a day. Or minocycline 50 0r 100mg. Expect 2 or 3 months to see result.. Usually these oral treatments are well tolerated.
Difficult choice. You'll need to get with a physician who's good at treating acne. Topicals are rough on everybody with acne. You'll probably get a systemic antibiotic such as tetracycline and a salicylic acid wash or retinoic acid prep or some other combination that you can tolerate. If you're this sensitive, the isotretinoin regimen may be far more than you can handle -- but if you can, it will be a huge help.
RoAccutane. RoAccutane, prescription only. Must see a dermatologist.