I get bouts of tachycardia when overtired, climb steep stairs/hills, under stress, or after hot showers. is this heart or asthma related?

Could be: There are many possibilities: dehydration, anemia, asthma medication (albuterol), the asthma itself, an unrelated heart condition, and others. Best to sort it out in person with your doctor.

Do you count: Your heartbeat to know if it is really tachycardia or just a pounding? It has to be over 100 to be true tachycardia. I see you have asthma so it could be your asthma and stress and activity sure could tip it off.