New betta problems - I was unaware of cycling before new tank

So I am experiencing a plethora of issues with my new betta. I hope he makes it out okay. I was unaware of the cycling process before putting him into the new tank. It’s small (1 gallon) and temporary. I am getting a 6 gallon tank from my parents this coming week.

Now for the issues: when I put him in his tank, a few hours later, I noticed he:

• became lethargic;
• goes to the surface for air I assume too frequently;
• laid on top of the water heater so his mouth was just below the water;
• won’t eat;
• has a small elevated portion on his body, similar to the picture on this page (I think my Betta has dropsy but I'm not sure?);
• later, noticed white cloudy stuff on top of only one of his eyes;

I assumed it was the water quality. I changed 50% of the water, got Ammonia Clear fizz tabs and Tetra Cleaning Bacteria and added an approximate portion of these into the tank. That didn’t help much it seemed. I thought maybe the temperature was slightly too warm (81 °F / 27 °C), so I turned off the heater. He’s no longer laying on top of it, but still goes up to the surface to get air, although the behavior seems less severe than it was. He occasionally makes bubbles. His nose is pointing up and his tail is pointing down. Kind of just sitting near the surface.

When he was in his fish store cup, I did notice he had white stringy poop. I thought this was normal until I researched these issues.

I’m not sure what to do at this point.