It is not a problem to bring common medications to Thailand. However, if you use strong painkillers, drugs containing narcotics, or drugs that affect the central nervous system, you will probably need a certificate from your doctor. Typically, drugs of this type are marked with a red warning triangle on the package.
If you are not sure, whether it is legal to bring your medications to Thailand, you should ask the Thai Embassy in your country. You will find a link to the embassy at Thai Embassy and consulates.
Of course, you can also buy your medications in Thailand. The prescription rules are not as strict in Thailand as in many other countries. Even if you are required to have a prescription to buy your medications in your country, you may be able to buy it over the counter in Thailand. You can read more in the Buying Medications in Thailand article.