Levoxythyrine and syntharoid are both examples of "T4" thyroxine replacement hormones (named because they have four iodine atoms) .

Another class are the "T3" thyroxine replacement hormones (with three iodine atoms - Liothyronine (marketed as Cytomel) is an example).

The T3 hormones are more potent than the T4 ones - trying a T3 one is an issue worth discussing with your doctor.

Apart from that, production of thyroxine is controlled by a hormone called Thyroid Stimulating Hormone (TSH), made by the pituitary gland. If you have not done so already, it would be worth getting your doctor to arrange for measurements of your blood TSH levels.

If they are abnormal that might indicate pituitary gland issues.