What did the nuclear stress test show? Did any of the stress EKG tracings show ischaemic changes? Did you have symptoms on the treadmill? Since you say your symptoms happen at about 140-150 bpm, an adequate stress study for your age should have taken you at least into that heart rate range (.85 X (220 - 38) = 155).
If no demonstrable ischaemia on stress EKG, despite symptoms, then I don't understand why your doctor thinks you have heart disease. But if your tracings showed exercise-induced ischaemia, and angiography showed no blockages in the major coronary arteries, you could still have microvascular disease, sometimes called Cardiac Syndrome X.
Hope this helps. Again I am not a doctor, just an educated patient.
Update on my condition. So, my cardiologist thought we should do an angiogram just to cover all our bases but he didn't think he'd find anything. After all, it had only happened to him once before in his entire career that someone would show completely normal with every test only to have a problem revealed by an angiogram.
So I'm lying there on the table getting the angiogram when he goes, "Well, you've got a blockage." Make that two times in his career. I had an 80% blockage in my left anterior descending artery right at the first bifurcation. The choice was stent of bypass surgery. Went with a medicated stent.
Physically, I feel pretty great. I had a stress test the other day and hit 90% peak without any angina pain. Mentally, I'm a bit wobbily but I'm working on it.
The moral of the story is this: no matter what your doctors say, keep pushing them. Though I love my cardiologist he immediately discounted any chance of a blockage in my heart because I have none of the risk factors (no smoking, no drinking, no drugs, not overweight, plenty of exercise, no history of CAD in family, normal cholesterol). You have to take control of your treatment. Luckily it worked out for me. Imagine if I hadn't kept pressing and had a massive heart attack in 2 years.