Can you get a skin rash from taking antebuse?

Yes you can. Since Antabuse contains sulfur - one can have crossreactivity with allergic reactions to bactrim, (sulfamethoxazole and trimethoprim) furosemide, sufanilimide, dapsone, etc.
Yes. Acne, skin rash, and itching are among the possible side effects listed for antabuse (disulfiram). If such rashes occur, one can return to the doctor prescribing the medication to see if the rashes are truly related to the antabuse (disulfiram).