Hi How Are You!! :) My TSH Levels Were 1.4

Hi how are you!! :) My TSH levels were 1.4 (slightly on the low side, and my T4 I think it was, or T3 (I know it was one or the other because both werent measured, were 13.2 so again slightly on the low side. I think it was T4. I was always very cold, ice-cold hands for the last three years, very tired, tanned hands, hoarseness, etc. Irregular periods as well. So I knew i had all the symptoms and asked my doctor should I get treatment and he prescribed Eltroxin - 50micrograms for 3 weeks followed by 75 thereafter. I feel SO SO much better, but am worried as I'm only 21, female and I really shouldnt have to take this. I lost a lot of weight, I had self-image issues around three years ago and I think all of that, including constant calories control damaged my thyroid. I'm just worried that eltroxin will eventually stop working or something. Also I geained a bit of weight over the past year or so, although I had still been restricting calories, and I'm wondering will Eltroxin help with this? :)
Thank you for all your help!