Take it from a mom with a daughter who was born without a thyroid gland - gimel is right-find a doctor who will moniter that freet3 level as well as the freet4 and TSH.
Even though TSH is a pituitary hormone that is affected by many variables to the extent that it is a poor diagnostic for thyroid problems, a TSH of 27, along with the symptom of tiredness, is more frequently associated with hypothyroidism, further testing is certainly necessary. If your daughter is being medicated based solely on TSH, that will not work for her. She really needs to be tested soon for the actual, biologically active thyroid hormones, which are free T3 and free T4 (not total T3 and total T4). In addition, lacking very much info on symptoms, I would also suggest that she be tested for the autoimmune antibodies, TPO ab and TG ab, and TSI.
Be aware that not all Endos are good thyroid doctors. Some specialize in diabetes. Others have the "Immaculate TSH Belief" and mostly want to test TSH, and only occasionally FT4. Hardly ever do they want to test for FT3, on the assumption that if they know FT4, then they can adequately estimate FT3. Frequently this proves to be false, because of T4 to T3 conversion problems, which occur even more frequently when on a dosage of T4 medication. In view of the vital importance of FT3, why not just test and make sure of the level.
If hypothyroidism is confirmed, then in my opinion the best way to treat a thyroid patient is to test and adjust levels of FT3 and FT4, with whatever type of medication is necessary to relieve symptoms, without being constrained by resultant TSH levels. If your daughter's doctor has a problem with testing and treating her in this manner, then you may as well start looking for a good thyroid doctor that will do so. Sooner or later, you will need one.
She may not present as overweight because it sounds more like Hyperthyroidism to me. Not a doctor so take my word at that. She could have Grave's disease. However, one of my friends tested high during a physical and had a goiter. Turned out to be an infection of some sort. Could also be hormones evening out.
I've been on Levothroxine for years with the hypo problem. Just be glad they caught it. I had my sports physical one year, they thought they heard a heart murmur and that my iron was low but I was fine. A month or so later during weight lifting, I nearly passed out. They found the Hypothyroidism and a Mitral Valve Prolapse during testing.