What is the importance of getting a complete thyroid test especially if concerned with fertility?

Must rule out prob: A thyroid problem would be an unlikely cause of a fertility problem, however it must be ruled out. This is quite easy, and blood testing will reveal if normal or not (most common tests for this called tsh, free t4, total t3).

TSH: Is the usual test you would do, if it is abnormal, then you need a thyroid panel, abnormal results could contribute to infertilty and abnormal results can cause problems with both mother and the developing fetus if not properly diagnosed and treated.

Thyroid & fertility: An underactive thyroid is a common cause of suboptimal fertility and it's easily corrected. Normal thyroid hormones in the mom are also important for normal development of the baby. An argument can be made that all women should have their thyroid tested in early pregnancy, or before getting pregnant, but no official organizations have made that recommendation yet.

TSH is best test: The TSH test is 10 times more sensitive for the diagnosis of hypothyroidism that the t4. The TSH is reported on a log scale so small changes in the TSH value are caused by relatively big changes in the blood level. This is a reflection of the pituitary being extremely sensitive to change in the T3 (liothyronine) level if you have symptoms it would be wise to seek treatment and get the TSH below 2.5 or lower.