Have you contacted the Thai Embassy or consulate? A document with a stamp from the embassy or consulate will carry more weight with the authorities on arrival.
U S Centers for Disease Control:
Yellow Fever Certificate
After immunization, an International Certificate of Vaccination
is issued and is valid 10 days after vaccination to meet entry and
exit requirements for all countries. The Certificate is good for 10
years. You must take the Certificate with you. Travelers who have
a medical reason not to receive the yellow fever vaccine should
obtain a medical waiver. Most countries will accept a medical
waiver for persons with a medical reason not to receive the vaccine.
When required, CDC recommends obtaining written waivers from
consular or embassy officials before departure. A physician’s letter
clearly stating the medical reason not to receive the vaccine
might be acceptable to some governments. It should be written
on letterhead stationery and bear the stamp used by a health
department or official immunization center to validate the
International Certificate of Vaccination. Check embassies
or consulates for specific waiver requirements.