If you are sure this is rain rot, which is a bacterial infection caused by d. congolensis, then you may need to have your vet administer systemic antibiotic to eradicate it. The bacteria live dormant in the skin and can become active whenever skin integrity is compromised. Prolonged exposure to dampness, abrasions, open cuts, or anything else that compromises the skin barrier, or anything compromising immune functions can precipitate active infection. Reinfection by bacteria on other horse's active lesions or on grooming equipment is possible, but only when the skin integrity is too compromised to prohibit active infection from developing. Vectors like flies also carry the bacteria between animals, and reinfection can occur that way as well. In some cases, secondary infection by other bacteria such as staph or strep may develop. Once this happens, injection of specific systemic antibiotics is the most effective way to deal with it.
If the infection has invaded deeper layers of tissue, then topical treatments will not reach it. The d. congolensis bacteria can usually be killed simply by softening and removing the scabs, using cotton pads soaked in isotonic saline to cleanse any pus, then using dry pads to pat the sores completely dry and leaving the sores exposed to air. If flies are a problem, a very thin layer of EMT ointment (collagen gel) will seal them out while promoting healing of the sores. Vetericyn is another good product to dress the lesions if needed. just exposure to air does the most good.
Be very gentle in removing the scabs, and don't do anything like currying which will drive the bacteria into deeper layers and spread the infection to wider areas. Dispose of anything that contacts the scabs and pus in a sealed container. They are laden with bacteria. This infection can be spread to humans and horses.
Don't use harsh chemical treatments like iodine solutions since this is not a fungal infection only affecting outer dead protein cells. Iodine solutions are appropriate for fungal infections, but not for d. congolensis infection, which is what causes rain rot. This infection invades living tissues and iodine solutions or other chemical treatments kill healthy cells , further disrupting skin integrity and providing more food for bacteria to feed on. Use 0.9% isotonic sterile saline to clean the lesions and remove the scabs.
Anything that you can do to keep the skin barrier healthy and intact and to provide optimum nutrition to maintain immune functions will be preventive. Frequent grooming, avoiding bathing with soaps that remove oils and disturb the bacterial flora and pH, and getting the coat dried out each day if there is rain will all help. Blanketing can promote rain rot by obstructing air flow and providing the dark, airless, and moist environment on skin that these anaerobic bacteria thrive in.
I would have the vet confirm the diagnosis of rain rot, and administer antibiotics if the vet advises it. Appropriate antibiotic one-dose injection is preferable to oral antibiotic treatment, and chronic infections can be rapidly cured with a single IM injection of procaine penicillin (22,000 IU/kg) and streptomycin (22 mg/kg). If this fails to completely eradicate it, then a single injection of long-acting oxytetracycline (20 mg/kg) can be admininistered.