Once the doc gets your thyroid levels under control, you'll be fine. I don't see any problem. Thyroid problems are fairly common. FWIW, I know several pilots holding first class medicals that have arterial stents! Taking thyroid meds is not a big deal.

You don't have anything to worry about. Here's more info that you might find useful:

AASI for Hypothyroidism
After initial certification by FAA staff doctors, subsequent renewals qualify for AME Assisted Special Issuance (AASI), a process that provides examiners the ability to issue an airman medical certificate to an applicant who has a medical condition that is disqualifying under 14 CFR Part 67.

The authorization letter received from FAA, granted in accordance with part 67 (14 CFR Part 67.401), is accompanied by attachments that specify what information the treating physician(s) must provide for the renewal issuance.

Examiners may issue renewal of an airman medical certificate if the applicant provides the following:

•An authorization granted by the FAA.
•Thyroid function studies performed within last 90 days.
•Medication information with comments about any side effects.
•Doctor statement regarding any other associated problems, such as cardiac dysrhythmia.
The examiner should defer to the AMCD or Region if:

•The TSH level is elevated.
•Symptoms of associated illness, such as dysrhythmia, have developed.