If this happened after a round of antibiotic you may want to to consider getting tested for C-diff? Especially, if it smells just as bad comming out the other end. The only other thing I can possibly think of, is if your food is not making it into the bowel and causing you to burp foul odors.
Did you get re-tested for infection after completing the antibiotic? If not, I think you should call your doctor and tell them your symptom(s).
Aside from that, I believe being stressed can make breath foul, so stress management would be something to pursue if that's an issue with you. Constipation can also cause foul breath, so taking some miralax (or a generic like clear-lax) might be something you may want to try to attempt deconstipation. Yogurt and parsley are two things that are supposed to help bad breath.