You might want to do a google search on ACCE and TSH. A few years back, AACE recommended that the TSH range be changed to 0.3 to 3.0. Many doctors are now realizing that a TSH over 2.0 can cause problems within the body. My advice to you is to get your TSH tested again, making sure its a first thing in the morning test. TSH is highest while we sleep, so you want to test near this high point. By 2PM, its at its lowest point of the day. If possible, also test free t4, free t3 and an antibody test.
BTW, I am hypothyroid. My first TSH came back at 2.6 and I was told I did not have a thyroid problem. 9 months later, the TSH was tested again and it was 6.8 and I finally got diagnosed. By that time, I had almost every textbook symptom. Was I hypo with the TSH of 2.6, probably, but he doctor only based the decison on that one test. Every symptom I had screamed hypo. Had it of been years ago, I probably would have got diagnosed earlier. There's too much of an emphasis on the TSH test. If hypothyroidism is suspected, more testing such as the free t4 and free t3 should be done. Otherwise we suffer with symptoms until the TS finally elevates and that's too bad.
It's a borderline TSH -- would consider testing TPO antibody (hashimoto's -- higher probabiltiy w/ mom's history and recent childbirth), if positive, then may be worth possibly considering levothyroxine -- but with a baseline TSH of 3.7 there may not be any benefit (as symptoms may not be thyroid related).