I just gave my almost 4 year old a dose of delsym (dextromethorphan) for the first time and she is asleep but seems restless and her heartbeat is elevated. is it bad?

If you can keep: her stable (no seizure activity, no somnolence, no high uncontrolled fever, no apnea, no confusion agitation) overnight by checking on her very 1-2 hours, and she appears to be breathing well, then I would let the heart rate be a little fast. It's most likely the antihistamine in the Delsym (dextromethorphan) that is causing the fast heart rate, and in a 4 year old they can do 130-140 heart beat for a long time.