I am sorry to hear of your worry. I was feeling tired a lot back in August and then found out that my blood pressure was running too high. Since then I have been on a series of medicines to get it under control and that has been a real journey. The stress of how the medications have made me feel is much worse than how I felt before. Ironic, eh? My body is very sensitive to medications and has not been very cooperative with side effects, etc.
My heart was beating very fast - 90 to 100 beats per minute right out of bed. The medication I am on now is a beta blocker and has done a good job of lowering my heart rate (57-90 BPM now depending on what I am doing) and my blood pressure is staying in healthy ranges. My blood pressure/heart rate appears to be related to adrenaline surges.
There are many conditions that could be causing how you feel, and yes it could be heart related, but that doesn't necessarily mean anything terrible. That is something that I have had to work through with my whole situation so I can keep my stress under control.
Only your doctor can really give you answers, and the good news is that you are going to be seeing him or her. I am glad to hear that it is not your asthma and that you have been able to reduce those medications. In any case, this is the place to talk about
it for sure.