I suffer from axiety and thyroid problems but I refuse to take medicine for my anxiety because I am sesative to medicine makes my heart race please help?

Is it hyperthyroid? If hyperthyroid, your anxiety and possibly the heart sensitivity are due to this underlying condition. Aggressively treating the thyroid should alleviate the anxiety - eventually. In the mean time there are other anxiolytics, a wide array. One can certainly be found different from what you initially tried - and yet be very effective and well-tolerated. Assumes that heart rhythm simple tachycardia.
Many choices. There are many options for treatment of anxiety. Not all have "heart racing" as a side effect. Talk with your doctor.
You need: . Workup of general medical issues (thyroid, cardiac),  psychiatric exam for identification/addressing of intrapsychic/psychosocial issues with  psychotherapy and use of community resources/support systems available & psychopharmacoeducation because "generalization" with anticipated response to medications per past experience limits the biopsychosocial approach/effectiveness. Consider biofeedback.