Prescriptions work differently in Thailand in that you do NOT need a doctors prescription to get medicines at the local pharmacies.
One does not have to travel far to find a local pharmacy, often family run with years of experience.
Simply tell the pharmacist what is ailing you and they will have an accurate prescription to cure you right away.
I have never had a local pharmacy fail to cure me.
Medicines are quite cheap in the local pharmacies as well. Many prescriptions only cost $1 or $2 dollars.
If you are taking expensive prescription meds from abroad, you might want to consul with your Thai doctor if their is a cheaper version here?
Else you can try the well known pharmacies like Boots.