Help determining what is wrong with my betta's fins

So I bought a betta fish and the first few days he was fine. Then, his fins started to fray around the rays. I assumed it would be fin rot, but his water parameters are normal, and I wanted to see if anyone else had an idea as to what it was. Since i believed it was fin rot, I tried treating him for a week with bettafix (recommended dosage) and aquarium salt (1tsp/gallon). Does anyone else have an idea as to what this could be and how to treat it. I currently have furan2, maracyn 2, and kanamycin on hand if necessary. http://imgur.com/a/22O0M 1:He is a delta tail betta. His fins seem to be disappearing and fraying around the rays. There is a slight grayish color on some edges of his fin at the edge 2:ammonia is under 0.02ppm, nitrites are 0, nitrates are 10ppm, temperature is 76-78 degrees depending on the day, pH is between 7.0 and 7.2 3:The tank is 1 gallon (I know it is small but it is the largest my college allows. I am unsure why), and has been cycled for 1 month 4:I am using a tetra whisper in-tank filter for 1-3gallons 5:He is the only fish in the tank. Orlando(my fish) is a delta tail betta with a body of 1 inch and fins approximately 2cm long. 6:I have had orlando for 3 weeks. I acclimated him by floating him for 40 minutes and then doing 50% changes of store water with my aquarium's water 4 times at 20 minute intervals 7:I had not added anything new by the time I saw the deterioration start. Once I saw it, I did a 100% water change and washed everything used in the tank with hot water (no soap)