Asthmatic with rapid heart beat and heart palpitations? What do you think it could be?

I am a recently diagnosed asthmatic. I have always had problems with allergies but the past year I've been having wheezing and shortness of breath. I am on several medications for my asthma and it has helped me somewhat. The past couple weeks I've been having rapid heart beat intermittently. My doctor first thought it could be due to my inhaler but even when I didn't use it, I still have a fast heart beat. Also when I wake up in the morning, sometimes my heart feels like it's fluttering and it will go away after an hour. I have noticed when I have asthma attacks my heart beat goes up, do you think it could be asthma related? Or could it be a separate issue?

have you been tested for a pulmonary embolism or emboli? Do you also get chest pain?