Suggest Remedy For Heart Ailments

I had a baby 18 months ago and previous to that suffered from Hyperthyroid due to a virus. I was suffering from significant tachycardia and excessive sweating at that time. RAI Uptake was done etc, Virus resolved rendering my thyroid now Hypoactive for the last 4 years. I am currently taking Synthroid 150mcg. I have been a runner my entire life however first trimester complications caused that to cease. I am not just getting back into it and training for a half marathon. I have noted that my heart rate even after 5 minutes of running is around 186 bpm. I went to my GP to have my TSH and T4 checked to be sure I wasn t over medicated. Everything was normal. His response to this high BPM was to add a Beta-blocker. I have leary of taking it because I have read it will greatly affect my performance while running. I also get a quivering type feeling here and there through out the day in my heart. I get extremely flush almost purple in my face when running. I m wondering if there could something significantly more wrong than the thyroid affect as my GP has mentioned. I asked for a stress test and he said I didn t need one. I am 34 years old, slightly overweight still from post-partum. no other medical conditions, no history of any previous medical conditions other than Gestational Induced Hypertension and ecclampsia which clearly has resolved and Gestational Diabetes which also resolved.