Where exactly is this pain - in the armpit, along your underarm?
Have you hurt your arm recently?
Do you have any pain at the back of your neck, along the spine?
DO you have any boils or blisters on your arm?
Pain that is burning in nature is usually due to an irritation of the nerve supplying that area - that is why I asked if you had injured yourself or have a pain in your spine.
It is possible that the nerve is being pinched or compressed under the armpit or by the muscles in your undearm. You will need to be examined for a proper diagnosis.
Meanwhile you can apply an icepack over the area for 10 minutes 3 times a day. Dry it off and apply a pain relieving gel like Tobricin over it. These are however temporary measures. Continue to take Aleve 500mg twice a day after food. If the pain continues for more than 3 days, please see a doctor.
I hope this helps.
Let me know if you need more input. If not, please click on the green"Accept" button on this page. A positive rating and adding a bonus will be warmly appreciated.