$US33.33 per day for 90 days is $3000, this is pretty tight, I don't think it can be done but others may differ.

The lower your daily standard of living anywhere in Asia the more likely to get sick from food contamination so you shouldn't aim at going too native, if you get sick from food contamination it can be pretty debilitating.

Chang Mai to Phuket is a long way, even Bankok to Phuket is a 12 hour trip by road, so it depends how you plan to travel inside Thailand?

BobMac, an Aussie, lives in Thailand and is regular on this forum should be along any time soon, I'd listen to his advice if I were you.