Im getting a sinus infection on left side and suddenly started getting sharp shooting pains in my left shoulder n down back of left arm.

Sinusitis: If, in fact, you actually have sinusitis, there should not be any relationship with pain into your shoulder unless you are are developing one of the infrequent but severe complications of this illness. It very much sounds as if you should be seeing a doctor asap. Hopefully this will turn out to be a minor issue, but would not want to risk your health over it. Good luck.