It does look like you have hyperthyroidism, according to your blood tests and your symptoms would bear that out. It would have been better if they'd done a Free T3, along with the Free T4 and TSH in order to confirm, though.
Hyperthyroidism is hyperthyroidism and is, typically, not categorized as mild or severe. You should ask for antibody tests to try to determine what the cause is. The most common cause of hyperthyroidism is Graves Disease, however, hyper can also be caused by Hashimoto's Thyroiditis, as well, which often starts out as hyper, then swings back and forth to hypo and/or normal before finally settling into permanent hypo...
The antibody tests to determine if you have Hashimoto's are Thyroid Peroxidase Antibodies (TPOab) and Thyroglobulin Antibodies (TgAb). You need them both, because some of us only have one or the other, while others have them both. The definitive test for Graves Disease is Thyroid Stimulating Immunoglobulin (TSI)...
There are a number of things that can cause the elevated liver enzymes. I've seen hypothyroidism listed as a cause, but not hyperthyroidism... You really need to talk to your doctor about these. It could be a one time thing due to inflammation from something else and often results like these need to be elevated much more than yours are in order to be considered a problem, but still must be investigated.