Hello!
Following a quick search on a database designed for physicians, I did not find any contraindication to the use of laser hair removal: neither in relation to the use of clindamycin, nor in relation to suppurative hydradenitis. Despite my limited expertise on the subject I would be inclined to say that there should be no problem.
In fact, several types of laser treatment would have been studied (over a dozen) to reduce the symptoms, hence some logic behind thinking that it might get better. Unfortunately, the data would not support a strong recommendation to suggest them, according to the American Academy of Dermatology.
Concretely if topical clindamycin proves ineffective (a first-line option for most situations) and the physician is certain of his or her diagnosis, he/she may opt for oral antibiotic treatment (rather than laser therapy).
In such a case it would be pertinent to discuss with the pharmacy, there are ways to send suggestions to the doctor depending on the progression of the problem, especially if the doctor may not have follow-up planned or is difficult to reach.
Hopefully this helps a bit
Don't hesitate if there are other questions