You have extremely poor husbandry, which is the main problem. That's obviously much more than a "bad" shed.

You say Neosporin is in short supply, does that mean that you have some? If so, use it!

Stop soaking him everyday. Did you soak him before he shed? If you did, that has the potential to hurt his shed process.

Why are they "PROBABLY" on 70 degrees? That's very cold. I'm assuming that's the warm side, I don't even want to know what the cooler side is. Probably? You have a UTH and no thermometer? That long scale peel is probably a burn.

Your poor snake.