My T3 (liothyronine) free is low 2.2 TSH and T4 free are normal my mom and 2 daughters have hashimotos and my thyroid is enlarged does this mean I have thyroid probl?

Hashimotos. You may have low grade hashimotos. With that family history and an enlarged thyroid it is quite possible that autoimmunity is slowly damaging your thyroid. But your thyroid has enlarged to compensate, and the normal TSH suggests that is compensating adequately now. Talk to your endocrinologist. You may become hypothyroid eventually, but it may not be for years.