No, i haven't had any acne breakouts related to the Botox although I suffered greatly when I was much younger. (I am almost 61 now.)
How old are you? Do you have a history of acne breakouts?
If you are getting breakouts, I would question how well your doctor is cleansing the area prior to the injections. Also, it might help to use an antiseptic cleanser such as Hibiclens or anything for acne prevention on the areas to be injected prior to going to the doctor to make sure the areas to receive the Botox are as clean as possible prior to getting injected.
Perhaps, your dermatologist could give you a good cleanser. Also, I would use the same cleanser for several days after your injections.
This might help prevent any breakouts. As an RN, I believe in prevention. I agree that taking an antibiotic year round is a bad idea. That is how bacteria develop resistance.
Good luck and let us know how it works out for you.