My partner (30m) experienced left arm numbness and face tingling that left within 5 minutes, but still has some shortness of breath (potentially panic attack related). should he go to the doc? worried about heart attack?

Those symptoms correlate with a neurologic event than a cardiac event. If all symptoms resolve by now, there is no need for urgent care or ER but he should see his family doctor as soon as possible.

Focal numbness and tingling can occur as a migraine aura, a brief transient ischemic attack, a simple focal seizure, BUT would be an unusual presentation of a panic attack. Since primary cardiac events can usher in secondary neurological symptoms, this too could be considered. See a physician ASAP, and get this diagnosed.