It maybe due to cough
Hi and welcome.
Yes, this may be caused by excessive cough since arm nerves may be irritated in this case. However, some other causes may be considered and it would be good to do lung x-rays to rule out pneumonia
If there is pain in left arm associated with chest pain
then you should get an ECG done and see cardiologist for further evaluation.
If this does not pull back after cough subsides then you should do neurological and vascular evaluation of your arm which includes neuro graphs and doppler ultrasound
Wish you good health. Let me know if I can assist you further.