If the antibiotic was given to prevent an infection, you usually only take it for a day or two, so you should be fine in a few days. If it was already infected, it may be longer. I would go ahead and dive if your not having any symptoms.
I was on various antibiotics for 3 ½ years due to a chronic prostate infection. I absolutely hate them, but some times there is no choice. Needless to say, in order to do anything, I had to do it while on them. Long-term use makes you fatigue and lowers your immune system. Best thing to do while on them, and for a week after, is to take acidophilus and restore your good bacteria.
I have never heard of an asthmatic having trouble breathing at the end of a dive if they didn’t already have trouble before the dive. But Asthma is really a symptom, not a disease. It is what triggers the asthma that you need to know. Many Asthmatics do better when around and in salt water. Chlorinated water is even better. Many of the U.S. best swimmers over the years were asthmatics that got their start when their parents put them in swimming to give them exercise. A good friend, who suffers badly, does great on filtered scuba air.
don