TSH is a pituitary hormone that is affected by so many things that at best it is only an indicator , to be considered along with more important indicators such as symptoms and also levels of the biologically active thyroid hormones, Free T4 and Free T3. So you should always make sure to be tested for Free T4 and Free T3, along with TSH. Also, since your TSH is above range, you should be tested for the possibility of Hashimoto's Thyroiditis, by testing for Thyroid Peroxidase antibodies (TPO ab) and if that is okay, then test for Thyroglobulin antibodies (TG ab).
If either TPO ab or TG ab shows positive, that is indicative of Hashi's. With Hashi's the autoimmune system erroneously identifies the thyroid gland as foreign to the body and produces antibodies to attack and, over an extended period, eventually destroy the gland. As this proceeds, the TSH level increases due to the diminished output of natural thyroid hormone from the gland, and replacement thyroid medication is required.
So please tell us about any symptoms you have.
Your TSH should be under 2. Also ask your doctor to test for antibodies