Is there is a blood test to detect an allergy to thyroid medications?

Does anyone know if there is a blood test or allergy test that can detect an allergy to Thyroid medications? I seem to be having difficulty getting regulated on thyroid medication and I can’t tell if the side effects are due to the medication side effects, dosing issues (not enough or too much), or a sensitivity to the medication (allergy of sensitivity). I have been prescribed Tirosint gel caps and then liquid, to see if the issues were related to a sensitivity to the fillers however the side effects from Tirosint were TERRIBLE. I have tried several medications. I was on Levoxyl but was getting pins and needles in fingers and toes along with the a lot of other effects, so I was just put back on Synthroid (I am on second week). Unfortunately, the side effects seem to be increasing and I am unsure if it is related to the dose (too high or too low) or a sensitivity to the medication. Does anyone know if there is a blood test or allergy skin test that can identify allergies/sensitivities to thyroid medications?
Thanks!