Hello prakashksilwal , i see currently you are having low blood pressure and a difference of blood pressure of 10 mm of Hg between your hands . Thyroid medication that you are taking currently rarely decrease blood pressure and that also within days as it starts working late i.e., it prevents formation of new hormones but do not inhibit the action current hormones in your blood . Difference of blood pressure could be a normal variant or could be a sign of early disease like peripheral vascular diseases, hypertension, diabetes, atherosclerosis , chronic kidney just to name a few. My advice to you would be if you are feeling lightheaded ness which is unbearable or trouble please stop your pressure medication and seek seek opinion from your primary physician at the earliest. I hope i have been able to clear your doubts. Take care