I agree with your second paragraph. The thyroid test is essential for anyone who suffers from depression. Quite often a doctor will put a person on antidepressants without performing this test.
The thyroid test measures thyroxine and thyroid stimulating hormone(TSH) levels. Be suspicious of a TSH level toward the high end of the normal range.
The normal range is just a statistical guide, to what values can be expected. It may not be normal for you. If hypothyroidism is the cause, a swift course of thyroxine will have one wondering what all the fuss was about.