Could be infection. Sometimes a skin infection called folliculitis occurs in armpits--looks like small individual pimples. If (but only if it sounds like this is what you might have) antibiotic ointment could help, but see your dr. If it's not improving in 2-3 days. In the future: avoid dull razors, don't share them, clean them well, and keep them dry in between use. Use an antibacterial shave gel.
Underarm rash. Underarm rash may have many possible causes, including allergens (agents that cause allergies), infections, autoimmune disorders, or other causes such as stress. I would first stop the antiperspirant but if that does not help see your local dermatologist.