Yes, I think 90 days is plenty. The normal dose for a urinary tract infection or ear infection is one Bactrim DS tablet twice a day for 7 to 10 days.
I suspect you will begin feeling better soon. Keep hydrated (drink lots of water) as this will help your system get back to normal and will help your body fight the acne-producing bacteria as well. Also, using one of the acne-fighting topical products available at pharmacies
can help keep your skin more free of bacteria
Not taking the the medication could cause a rebound in your acne eventually, but not necessarily. Using diet, good hygiene, and the over-the-counter topical products may just be enough. And if it does come come back in the future, you might use a different antibiotic. That is something you and your dermatologist will figure out.
I hope it goes away and stays away, as it sometimes does.
I hope this information has helped you. If you have more questions, just ask, otherwise, please "Accept" the answer.