TSH reflex free T4 test = 2.51 (normal range 0.35-4.50). I've read hyperthyroidism still possible if TSH normal. Do I need another test?

TSH. Highly unlikely. That said, your doctor should have ordered TSH and T3 (liothyronine) as well as T4. Please go back to him/her or if you are not satisfied have a friend or family refer you to a better doctor.