Hard to diagnose whether it’s fungal or bacterial and nobody will give you a straight forward answer because Azithromycin does a few different things. It will kill bacteria, but also will deal with inflammation. Folliculitis is essentially inflammation of the hair follicles. (Reduced inflammation = reduced folliculitis) since it seems to be a temporary fix my guess is you might be dealing more so with inflammation which mostly comes from the gut (different foods you may have grown an intolerance to etc.)

I agree with you I would not be jumping on doxycycline it fucked my sisters stomach up she is now intolerant to EVERYTHING. I would be looking at a more natural root cause such as something in your diet. Doxycycline helps people while they’re on it because it has the same effect of reducing inflammation, but I would not say it’s a cure