The Tinactin is an antifungul and when you use the spray it helps dry it.
And yes, pick off those scabs. The rain rot is harboring underneath that. Its a great little environment for the bacteria to live in.
Do you have coolers? Blankets? Anything? If so theres no reason you can't bathe a horse. Give a bath then toss 2 coolers on. The first one will keep them warm while pulling away water. The second one on top will pull the water from the first one so that they dry faster and don't get cold.
At the least wash it with a bucket and sponge in the affected area. If you don't wash it, its not going to go away.