It will be okay...I really,really, really doubt that you will faint. This is such a common symptom of us anxiety sufferers! I have been feeling faint every day for the past week off and on. Whenever I am home alone I get this fear that my heart is going to stop or I am going to pass out. I was scared to go into work yesterday in case I fainted in front of everyone! Once I got there, I got to working and forgot all about it. It just kind of assures me that it is all in my head when I realize how when I think about it, I feel it, but when I am preoccupied the faint feeling goes away (usually)!
I also can relate to being afraid of getting your heart rate too high. This is also a problem of mine at the minute. When I have been going to the gym I panic as soon as I start to get a little out of breath. I think things like "Do they defibrillators here for when I pass out and my heart stops?" and I wonder if anyone knows CPR. I don't tell ANYONE these thoughts because they sound silly even to me but I can't help but think them!
So, I know how you feel to be frustrated with what is essentially hypochondria. I think this is what most of us on the board suffer with. The good thing is we are not in this alone and so many others understand EXACTLY what we are going through. We are not crazy or dying, we are just suffering with an affliction that is quite common in our society--anxiety.
And well, I've heard that anxious people are much more likely to be highly intelligent and creative, so at least we've got that going for us!
Take care...you will be alright. As my doctor says, there is no reason we HAVE to feel this way...there are ways to control it, and some ways work better than others for each of us. So....maybe that therapist isn't the right one for you? Either way, just try to remember that the chances of your heart stopping or you fainting are miniscule. These are things I need to remember myself, I know, but they are true.