Hey how is your betta? I was thinking that more water changes would really help. I am not sure if you still trying to cycle your tank. But my advice 2.5 gall really difficult to cycle. Just like someone already recommended to do 50% and 100% weekly changes. It really easier for you and better for fish ... It just you need to acclimate betta to the new water temp so you don't shock him with drastic temp difference.
And if he still sick give us update you might try to use aquarium salt depending on the symptoms he might have.