The only tests that can pick up thyroid activity before the medical test does are home tests.
1. Take your body temperature (under the tongue better) before you get out of bed in the morning with a mercury thermometer (hard to find anymore but they are more accurate). If your body temperature is always under 37 C, it indicates an underactive thyroid.
2. Put some liquid iodine (from natural food store, the ingestible type) and apply some on the skin of the throat (on top of your vocal cords is where your thyroid is). If the iodine is all absorbed in less than 10 minutes it means it is underactive. If it takes more than 10 minutes, it has a normal function. If it causes irritation to the skin and tingling, it has a tendency to be overactive. Do not take the liquid iodine internally unless you know how, because it is very concentrated and in some cases it causes more stress to the thyroid and can make it crash (too drastic of a change, not a gland that like drastic treatments).
Here is a text on that subject.