Her TSH is above range (TSH is counterintuitive - high TSH indicates hypo,
low hyper), and her FT4 is in the very
low part of the range, both indicating hypo. You are correct, Synthroid is used to treat hypo. Her symptoms are also typical of hypo.
The choice of whether to see an endo is a personal one. A PCP can manage many thyroid conditions if he is well-informed regarding thyroid.