I would look for someone who specialises in making shirts!
I have a very good tailor who made several suits and trousers for me; top quality in terms of fabric, style and finishing. However they also offered shirt making, which I tried once. It was rather disappointing... The collar was way too stiff and the quality of the (cotton) cloth was mediocre.
I found the selection of suitable cloth (with the right weave and style) for dress shirts seems very limited and a bit old fashioned.
As said, unlike the high-end woolen (cashmere-like) cloth woven in Italy that I have been offered for my suits here, all the cotton cloth for shirts I have seen in Bangkok (Sukumvit) was rather unsatisfactory.