First time betta owner; really need some advice on helping the poor guy :/

I am feeling awful; I think our betta is pretty sick due to my failure to do enough water changes. This is my first fish, and was unaware that 1/2 gallon tank (sold as betta tank) was way too small for him, and also I feel awful because I was only changing his water every two weeks for several months. His water started to get a slight orangish tint to it, which is when I got online and realized my mistakes. I moved him to a 2.5 gallon tank a month ago and have been doing water changes weekly. Unfortunately, his health has taken a turn for the worse about two weeks ago, and I feel horrible for making the poor thing suffer; I hope it's not too late.

Here are his symptoms:
-hasn't eaten in over a week
-flaring gills and gasping for air at the top of the water, looks like he can't breathe.
-stayed at the waters surface with top of head and mouth out of water for a week, have found him laying in side on the bottom and gasping.
-kind-of curved look to his spine
-shrinking fins, also has little white balls forming on the tips of his fins.
-lethargic
-although he was already whitish-pink, he looks even duller, has some small black spots on head, and his scales just don't look vibrant or healthy.

Here's what I've done as far as treatment so far:
-1 week ago: began doing water changes every other day, put him in a warmer room of the house. He didn't seem any better.
-3 days ago: began doing daily water changes, and adding aquarium salt (dissolved, about 1tsp in his 2.5 gal tank at a time. I haven't put more than 2tsp in at once/without doing 100% water change. Bought a filter, but stopped using it after 6-7 hours because I was worried it would further damage his fins. The next day, we found him laying on his side on the bottom of the tank, and flaring gills wide as if he couldn't breathe. Got thermometer, and keeping him in front of the heat register( temp ihas pretty consistently been about 74degrees since).
-2 days ago: did another 100% water change, and took out all of his rocks, plant, and hide, and boiled them for awhile. Scrubbed tank out with just a paper towel, then rinsed the tank with boiling water several times. Yesterday he seemed a little more active, and havent seen him at the bottom since this water change. Maybe not quite as dramatically gasping for air, but still sitting at surface, and still lethargic.

I would appreciate if anyone could help me figure out WHAT he's sick with, and what I can do to help him. I hate seeing him suffer, especially knowing it is very likely because of me. Thanks so much.

Sarah