In trying to assess a person's thyroid status, the most important indicator is symptoms. Your daughter has symptoms that are frequently related to being hypothyroid. The next useful indicator is test results, mainly the biologically active thyroid hormones, Free T4 and Free T3. TSH is a pituitary hormone that is affected by so many things that it is useful only to identify overt hypothyroidism and to distinguish between primary and central hypothyroidism.
The Total T3 test is a measure of all T3 in the body, most of which is bound to protein and therefore not biologically active. In the future you should make sure they always test for Free T3, since that is the thyroid hormone used by all the cells of the body to produce needed energy.
Your daughter's Total T3 is only about 21% of its range. If this is comparable to her Free T3 level then that is typically too low and indicative of hypothyroidism. The range for Free T3 is far too broad. Free T3 is best in the upper half of the range. Along with that, her Free T4 level is above range, which is inconsistent with her relatively low Total T3, and her TSH level. This makes me suspect that her body may not be adequately converting T4 to T3, which would account for having hypothyroid symptoms. Conversion can be affected by a large number of variables, with ferritin levels below 100 being a major factor.
I recognize the difficulty with getting blood drawn for tests, but I really cannot even suggest a course of action without further testing. I do suggest that you discuss all this with her doctor and reach agreement on a plan for testing, at first opportunity. If it were me, I would insist on tests for Free T4, Free T3, Reverse T3, cortisol, Vitamin D and ferritin. With that info in hand and knowledge of her symptoms, you should be able to determine a plan for treatment. Note that a good thyroid doctor will treat a hypothyroid patient clinically by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms, without being influenced by resultant TSH results. Symptom relief should be all important, not just test results.