>Can they be felt everyday even when not feeling anxious about anything?
Absolutely! Stress symptoms can show up at the time of stress (the fight or flight reaction), or they can show up well after the fact due to gradually built up stress. As an example, you don't have any ill effects the first time you clench your teeth, but if you do it habitually, you'll start getting headaches.
Just because you don't feel anxious doesn't mean you aren't still reacting to stress. If you've already had fairly conclusive tests for your heart (barring an ultrasound by a cardiologist, which you probably don't need, I'd say you're good) then when you see your doctor, you should mention that you're worried about your heart and ask him for advice about anxiety.
The big thing is that if your doctor doesn't know that you're worried, he'll diagnose your symptoms and maybe make a passing comment about stress. In my experience, you're not likely to get a sympathetic reaction from the doctor unless you let him know that you're anxious and he should consider mental causes. Anxiety is a symptom too, and adding it to the list gives him more to work with in helping you solve the problem.