Sorry about your heart worries. I can empathize.
My Mom died of sudden cardiac death at age 59. When I had my annual physical at age 50 my primary care doctor recommended a nuclear stress test and I did not protest. Frankly, I did not take the radiation exposure into account when I agreed to the test, but should have. I had previously been examined by a cardiologist who did the usual EKG, echocardiogram and 24 hour monitor and said all was clear. That should have calmed my mind. But, I went ahead with the nuclear stress test. I remember sitting in the waiting area with a bunch of much older individuals, most of whom seemed rather frail or ill. When it was my turn I got on the treadmill and the cardiologist supervising the test asked me about 5 minutes into the test why I was there. I told him about my family history and he said everything looked fine and seemed to imply the test was a waste of his and my time, particularly since I had cleared all the previous heart tests.
As a patient with Crohns disease, I was exposed to a considerable amount of radiation in my teens and early 20's, as that was the only way they could monitor inflammatory bowel disease before the invention of scopes. I am sure my lifetime exposure to radiation is way high and should have thought twice about the nuclear stress test. However, I am currently age 62 and (knock on wood) in relatively good health. Most of my illnesses are in my head.
I don't envy your position of having to decide on the nuclear stress test or not. I can tell you that a clear test result will give you peace of mind for a short time, but was the exposure to radiation worth that short-term relief? At age 35 I guarantee you that additional x-ray testing will be necessary in your lifetime. I just needed an abdominal/pelvis CT scan which found a 1 inch kidney stone, so there was more radiation exposure, but it was necessary. Personally, I would suggest you limit your radiation exposure at age 35 unless it is absolutely necessary. Then, again, by the time you are 60, I am sure they will have invented a way to conduct tests using much less radiation than today.
I would recommend against the nuclear stress test if all your other heart test results were okay. Of course the cardiologist will recommend the test. They also always say the radiation exposure is minimal, but it is your body and not theirs being exposed.