You don't "HAVE" to get your thyroid tested, but since hypothyroidism is a major cause of tinnitus, I'd think you might want to rule it out.
In addition, hypothyroidism often goes hand in hand with type 2 diabetes and rheumatoid arthritis being an autoimmune disease, as is Hashimoto's Thyroiditis (most often associated with hypothyroidism), that would be one more reason to rule out/confirm a thyroid condition.
Do you have other symptoms of hypothyroidism? If so, which ones?