Hi Lung Per,
you could make a start with this company:
http://purion-thai.com/start.asp?nav1=a1&nav=a2. According to their website, they're based in Hua Hin and, although their prime business appears to be to sell you a system, they do say they have water testing facilities.
I have just had my well water tested, though not in Thailand. The test cost me the equivalent of 1000 baht.
To determine the quality of water for drinking, the lab I went to tested for manganese, arsenic, iron, fluoride, nitrate, nitrite, chloride, sulfate, phosphate, turbidity, pH, conductivity, total hardness, e. coli and total coliforms.
The results showed hardness, e.coli and total coliforms to be above the acceptable limits.
I have connected a Sawyer Point One filter kit to my incoming water supply and this filters out up to 99.99999% of all bacteria according to US standards. The filter is said to be good for filtering up to 1 million gallons of water (
https://sawyer.com/products/sawyer-pointone-one-filter).
Hope this helps!