What does it mean if the results of my thyroid function test are: tsh is 6.5 and the t4 is 19.5?

Thyroiditis: Very high T4 suggests release of stored thyroid from the gland versus overdose of t4. Inflammation of the thyroid in hashimoto's thyroiditis can make the gland unresponsive to tsh. Talk to your doctor about your symptoms. Propanolol or other beta blocker may be necessary to get you over this acute phase.

Repeat the labs: It's unusual to have both a high TSH and high t4. On the next test, i would do a tsh, a free T4 and T3 (liothyronine) instead to rule out confounding factors. Thyroiditis should give you a low TSH instead of high. If the repeat test is just like above, high tsh, high free T4 (and you are not on a drug called amiodarone), you might need to get a MRI of the pituitary. Hopefully it's just a lab error.

Units of Measure: Tsh is usually measured in uu/ml. The 6.5 is slightly elevated. A total T4 would be elevated if measured in ug/dl, but low if measured in nmol/l. Any anti thyroid antibodies? It would be helpful to measure a free T4 and free T3 (liothyronine) in this case, also repeating tsh. If the ft3 & ft4 are high and TSH still elevated also, thyroid hormone resistance should be considered. It is very rare; different types.