Underarm burning pain has several possible causes. It could be nothing, or it could be serious. As with any medical problem, be sure to see your doctor to determine the exact cause of your pain.
Burning sensations in the skin are known as paresthesia. Any type of tingling, burning or numbness can indicate a damaged sensory nerve. Causes typically include a nerve injury or a disease affecting the nerves (one serious example is multiple sclerosis).
The burning pain could be a result of the deodorant you're using. Some people are sensitive to the chemicals used in common deodorants. Try switching brands or going without deodorant for a few days to see if the pain subsides; a dermatologist can help you find a product that won't irritate your skin.
A burning or aching sensation in the underarm area can be a symptom of swollen nymph nodes or tumors in the breast. Do a breast self-exam and see your doctor right away if you find a lump.
If you've had surgery in the areas around your underarms (e,g., breast or shoulder), there could be scar tissue or a pinched nerve causing the pain. Check with your doctor.
If the problem is skin-deep (such as irritation from a chemical), your doctor can prescribe a cream to ease the pain. You probably won't be able to wear deodorant for a few days, or you may be given a prescription formula to use. If the pain is internal, treatment will be based on the cause.