What may be normal for one person may not be normal for another. We are all different. You need to find a dr who is sympathetic and knows and understands about the thyroid and it's effect on moods, weight etc. It is IMPORTANT you get copies of your thyroid results so YOU can monitor how you feel and how you are at what TSH level.
For me, I am at my absolute optimum health when my TSH level is between 0.04 and 3.0. If my TSH level goes higher than 3 then I start getting depressed, weight gain, cold etc. My GP knows this and we manage it together. Just because you are within "normal range" it may not be normal for you. If you are at the upper level of "normal" then you obviously have room to move and your oroxin or thyroxin could be increased. Find a GP who understands this and works WITH YOU and you will be fine!
Good luck
Suexx