If you have been diagnosed with hypothyroidism, you should be on a prescription thyroid replacement medication, not an OTC supplement like Thyrostim, which may not work at all, because it has not thyroid hormones in it.
Have you been tested for Hashimoto's? If so, the iodine in Thyrostim is contraindicated as it can make the autoimmune reaction worse, which may be making you feel worse.
If you haven't been diagnosed with a thyroid condition and have symptoms of hypothyroidism, you need to get tested for Free T3, Free T4 and TSH to determine actual thyroid function, along with thyroid antibodies, Thyroid Peroxidase Antibodies (TPOab) and Thyroglobulin Antibodies (TgAb) which will tell you if you have Hashimoto's.
Maybe never. As far as I know a thyroid glandular bought over the counter cannot contain actual thyroid hormones T4 and T3. Note what it says below.
"Thyrotsim Tablets by Biotics Research contain vitamin A‚ trace minerals‚ iodine‚ and specific blends that combine nature and scientific research to promote thyroid health." Nothing there that would really help unless your are deficient in iodine, which is an unusual occurrence here.
Please post your thyroid test results and reference ranges shown on the lab report so that we can help assess your status.