Answer:
The treatment prescribed is strange, as a bursitis of that kind is very rarely bacterial in origin.... I am puzzled at the fact that no antiinflammatory treatment has been prescribed.
Regarding diving, however, the situation is not much likely to be negatively affected by normal conservative diving. The antibiotic treatment per se, if not generating any adverse effects, presents no contraindication to diving and the risk of increased inert gas uptake in the affected area, due to the increased blood flow generated by the inflammation, should be considered in this case, more potential that real, regarding normal recreational diving.
The only caution might be of mechanical nature ( pain due to mechanical stress ) and of possible diagnostic confusion with Decompression Illness (pain after diving interpreted as DCI related, even if generated by the bursitis) with risk of unnecessary chamber treatment.