The other thing you have to face is that your body is not in condition if you are 175lbs at 5'. Walking will certainly help to build up your condition, but until that happens, your heart rate is going to seem like it is running at exaggerated rates. You only said your rates were over 125 bpm, but you don't say wahtr the rates are. Does your rate get faster over time or does it just "jump" and take off all of a sudden?
Did you have more than just your TSH tested? Did they also check FT3, FT4 and antibodies? Some people when first starting on a thyroid med can have the heart palps or fast heart rate. It's your body getting used to the med. I'm a little surprised your Dr did'nt start you off on .25 mgs for a short time. Some do and some don't. I just think it's easier for the body to adjust when starting on a small dose and working your way up. You might want to give your Dr a call to say what's going on with you. 125 is not bad when your walking. I think your just not used to the meds yet.Normal resting heart rate is 60 to 100.