Hello and welcome – hopefully, others here can chime in with their experiences. I do know that being hyper or hypo can affect the nails. Have your thyroid levels been normal and stable all this time? For patients who are stable and feeling well, TSH testing is the primary measure used for dosing of replacement hormone, but since you are having this issue, it might be worth checking out T4/T3 if it’s been a while.
As far as I know, nail issues are not listed as a side effect with Synthroid (assuming you are on the correct dose), but you could ask your doctor about potentially switching to another product. (Just make sure to re-test thyroid function in a few weeks to make sure the dose is correct.) Also, some people are sensitive to the color dye in Synthroid – another option might be to have your doc prescribe the dose without coloring and adjust your prescription accordingly.