We are blessed in Thailand that we can get cheap blood tests at labs in most provinces without doctors referrals.
If you want to check for Haemochromatosis you can go to a local lab (Krabi - https://maps.app.goo.gl/F4ZrRouz9fCbXwSL9 )
Request a Ferritin test. It should be around 500 baht. If this is in range then it's unlikely you have Haemochromatosis and are loading Iron.
If it is high I would then ask for Serum Iron and TIBC tests (about 500 baht each also). from these 2 tests you can calculate your Transferrin Saturation (TSAT) by Serum Iron / TIBC × 100 = TSAT
With high Ferritin alone it's worth taking the results to a Haemotoligist. However if the Serum Iron and calculated TSAT are also high then it's a stronger indicator.
If the Doctor suspects it they should take some blood and send it to Mahidol University genetics lab in Bangkok for DNA testing to confirm it (This test is more expensive).
Of course you can just go to to the Hospital in the first step but you will pay inflated prices for the same tests and have to convince the doctor to do it in the first place. I have had good experience with Haemotoligists in Bumrungrad and Bangkok Pattaya Hospital and terrible experience with the one available person in the whole of Phuket.