Hello and welcome to healthcaremagic
I would keep a possibility of bacterial infection of the hair follicle/furuncle and surrounding
cellulitis.
-Axilla normally had a lot of bacterial flora and also there is constant rubbing/friction during arm movement.
-Sweating in hot humid weather conditions is another reason favoring bacterial infection in this area and
-Shaving in this area is which can also provide a portal of entry for bacterial infection.
If I was the treating doctor I would have advised an empirical oral antibiotic for a week OR 10 days (My choice of oral antibiotic would have been
Amoxycillin 500mg in combination with
clavulanic acid 125 mg, thrice daily, for a week OR
Cephalexin 500ng thrice daily OR
Cefadroxil 500mg twice daily, for a week). That would take care of the infection.
An OTC pain killer e.g ibuprofen once or twice daily would help you deal with the pain.
If the infection does'nt respond and the swelling increases in size OR there is development of fever and chills, then it might be the sign of formation of an abscess, which needs to be incised and drained.
regards