Your high TSH was an indication of the possibility of an autoimmune disorder called Hashimoto's Thyroiditis. With Hashi's the autoimmune system erroneously identifies the thyroid gland as foreign to the body and produces antibodies to attack and eventually destroy the gland. As this is happening the output of T4 and T3 from the gland is gradually diminished and the pituitary starts increasing the output of TSH in a vain effort to stimulate more T4 and T3.
With the lab order for TSH with Reflex to Free T4, I don't understand why tests were done for Total T4, T3 Uptake, and Free T4 Index. The tests you got are not nearly as useful as a Free T4 and Free T3, which you should make sure to get every time you go for tests.
Hypothyroidism is not just a damaged or diseased thyroid gland, but instead it is correctly defined as "inadequate T3 effect in tissue throughout the body due to insufficient supply or, or response to, thyroid hormone". So it is the TISSUE T3 EFFECT that determines your thyroid status. Since there are no direct measures of your thyroid status, including bood tests, indirect measures must be used instead. Of those, the best is an evaluation for signs/symptoms that are typical of hypothyroidism. At the time your doctor decided to start you on thyroid med, what symptoms were you having? If you want to use a survey for symptoms, try this one. Just check the ones you had and it will give you a total score.
Once you have completed that, let us know the score and we will discuss further. By the way, it unlikely that your current problem with constipation is due to the Synthroid itself. Much more likely is that the med reduced your TSH, and also reduced the output of natural thyroid hormone. Since your serum levels are the sum of both your natural thyroid and the thyroid med, Free T4 and Free T3 levels don't start to rise until the TSH is basically suppressed. Only then will further increases in med dosage stat to raise your serum levels..