My right armpit smells even after a shower and putting on deodorant. what could be the cause?

See a skin doctor: it might be a abnormal sweat glands or a hidden infection or a infarcts skin tag Either way you need to see a doctor for evaluation and treatment

See doctor: The fact that only one arm is involved makes me concerned yo may have an infection in hair follicles. Do you shave this area? You should be seen by your doctor. Good luck.