I used to take Levothyroxine for hypothyroidism -- don't anymore/currently (T4, the thyroid hormone that is Levothyroxine, binds with estrogen and I am a perimenopausal woman, so this is not weird -- as my estrogen levels have declined, my semi-functional thyroid is coping better with my body's demands). It's been a long time since I needed to look this up (and I am not a medical professional, etc. etc.) but my recollection is that only the thyroid can make T4, which is a largely stable/unused compound until the body needs it, then the thyroid and some other organs (kidneys? I forget) have the ability to turn T4 into T3 which is the "usable" form of the hormone, then the body uses it up and it is gone.
Levothyroxine is just T4. This works well for many people and is relatively easy to dose and take because the body can let appropriate amounts of it sit around "in the system" until it is needed for T3. OTOH, some people seem also to have trouble converting T4 to T3 and find they do better taking a product that contains both (Armour) or a T4 product + a T3 product (Cytomel). Things that contain T3 generally have to be taken twice daily I believe, and are harder to get the dosage right.
Unfortunately I don't think you know until you're trying, which group you're in. I tried both (Levothyroxine and Armour) at different times and found the straight-up T4 worked better for me.
That said, having your thyroid out of whack is really, really annoying and leads to all kinds of nutty symptoms. So getting problems addressed is probably worth doing. And yes, the medications are usually pretty darned cheap.