What could be causing pain when I strain or cough under my right armpit and breast muscle?

Hello and thank you for sharing your question.
Even though the car accident happened a few days ago, the pain could have been caused by a subtle injury. For example chest pain can cause referred pain in the arm. Referred pain is pain felt in a different area the actual site of the injury.
When the air bag went off, the muscles in your chest took a good hit. So now it is probably sour but you are feeling the pain in your armpit.
If it worsens over time however, there could be something more serious going on.
Faith