Hello, @Israel. I’ve had Hashimoto’s thyroiditis for many years, so I’m fairly familiar with thyroid lab test results, though I’m not a doctor - just offering my opinion.
Your high TSH indicates that your thyroid is actually underfunctioning - producing a lower amount of thyroid hormones (like your T4 hormone in the lower end of normal), which causes your body to produce more TSH to try to stimulate the thyroid to produce more hormones.
Personally, if it was me, I would ask for thyroid antibody testing - there are two antibodies, thyroid peroxidase antibody (TPO) and thyroglobulin antibody (TGAb) - especially if you have symptoms of hypothyroidism. Autoimmune disorders do tend to cluster sometimes, so if you have type 1 diabetes (autoimmune), you are at increased risk of developing other autoimmune disorders. If you are positive for antibodies, you may have Hashimoto’s.
As mentioned above, you might need a small dose of T4 prescribed to help bump up your T4 number (which would hopefully help bring down the TSH). I would ask for this if you are having symptoms, as it may improve your quality of life by easing the symptoms.