Sorry my post was so chaotic last night. I only had a few moments before all my internet control programs were going to kick me off.
Anyways, I'm glad your test results came back good

I used a lot of meds with my betta and it kept coming back, and it seems like he was on meds before I got him too, so I'm not doing meds with him anymore. I tried maracyn and marafyn2 (in conjunction) and the first time it worked well, but it came back, and the second time it did not work at all for me. A lot of others have had good results with the maracyns. After his last round of meds (I used super sulfa that time) I added 1 teaspoon of Aquarium salt to his 3 gallons. This is working out very well for him now. The rot came back only once so far, and that was from a strange cold night where the temp dropped 20* more than regular nights, then back up again. With the salt he healed right up, and he's still continueing to heal. If you want to try meds, I think most types would be okay. Stay away from melafix tho. Some bettas have very bad reactions to it, and it usually doesn't do much if there is an actual infection going on. All it really does is speed healing of open wounds and torn fins. And I swear, all the petsmart workers around here try to sell it to me like its an elixer. They even recomended it for my goldfish that had hole in head disease. I TOLD them the meds needed a certain chemical in it, but they insisted x_X Anyways, you can also try some aquarium salt instead. 1 teaspoon for the tank for right now, and be sure to dissolve it completely before adding. Be sure you have a container of his old water ready in case he has a bad reaction (some bettas do with salt as well). I am so paranoid whenever I add any med to a tank I watch them for at least a half hour with non medicated water standing by.
I'd start with a medication since you water looks good, there could be a type of infection. Most meds are in compressed tablets. Crush one and divide it accordingly so you will have the correct dose for 3 gallons, and save the rest for later. (EX: if you need 1 tablet for every ten gallons, crush and divide into thirds. Add the 1/3 to the tank, and store the rest.)
Yes, how cold is his water? Does he have a heater to keep the water at a constant temp? Any sudden temp changes? Temperature can be a factor as well