Thanks for posting your query.
From what you have described this is probably a local pain due to either an injury
You haven't mentioned for how long you have had this pain. Was there any injury or strain to the left hand?
It is most probably not a cardiac pain as cardiac pain usually starts from the chest and then radiates to the jaw and left arm.
There is no cause for worry.
You can try applying some local gel like Volini
Pain Gel on the arm three times a day.
If the pain continues or increases in severity or the chest pain
recurs then you will most probably need to consult a cardiologist
who will examine you to rule out cardiac causes.
Hope I have answered your query.