Getting prescriptions in Japan

am thinking about teaching in Japan within the next two years (COVID restrictions depending). I have hypothyroidism and take levothyroxine medication orally everyday. I was wondering what steps you would need in order to get the correct medication and dosage in Japan and what pharmacies would be best for foreigners? Would I need to find a Japanese doctor since my prescription might not be able to be transferred internationally?

Yes, in the long run, you’ll need to find a doctor in Japan.
I sound bring enough medication for a few months initially and start searching for a doctor as soon as possible after relocation (and after enrolling in health insurance). Bring your old prescription to show what is your current dosage regimen but your new physician will do likely new tests before doing a new prescription for you.

Yes, initially you might want to bring a few months’ worth of medication. You might have to look for a doctor in Japan - possibly one certified by Japan Thyroid Association - to get prescription thereafter (their website has a list of those doctors across Japan).
Maybe it would help to get your current doctor to write out your medical history so far, with the dosage and everything, so that the doctor in Japan (they would want to give you a full check-up anyways but) will have good reference information to rely on.

Be warned that if you plan on bringing a few months, by law you have to file for special paperwork before coming to Japan. You can bring a month supply without filling in paperwork, just bring prescription just in case, but you don't need to declare it.

I have the same condition and it's easy to get the medicine you need, I got mine straight away.

Bring your prescription and maybe a box of your current medicine(you might not need them, this makes the language barrier a bit easier) to a doctors clinic, I went to a 内科 naika, trust me they are everywhere you will not have trouble finding one.
Mention you have a thyroid disorder and you need to continue receiving the medicine. They will likely comply and give you a first months supply and arrange for you to have a blood test next time to check it's ok, then they will continue to see you regularly to keep giving you more medicine.

I have been living in Japan and moved twice and had to visit two different naika because of moving, they both followed the same procedure

Thank you for your responses. I am currently working on my TEFL certification. When/If I secure a position in Japan (preferably as a JET), I will talk to my doctor about all the documentation I will need and make sure I have enough prescription for a month, if not more (with proper application approval).