Also...I know you maybe think you will be spoiling his fun, but try if you can to discourage him from doing too much digging in the dirt with his nose. Distract him with a frisbee or toy, or a walk.
This is possible. My dog got obsessed with digging for moles. It was playing havoc with the skin on her nose! I gently but consistently prevented her doing it, by distracting her. I was sure it would stop her enjoying herself in the fields, when I kept having to tell her "no" as soon as she started digging, but I immediately followed the "no" with a frisbee game. It worked and she doesn't seem to miss digging for moles so long as she's having other fun.
Well, there may be others who will have good suggestions and a little less drastic than the one I'm about to suggest....
It has been discovered that having your dog's nose tattooed BLACK can protect permanently against sun-damage. (however with already sore skin, this is maybe not a good idea right now...)
Aloe vera sounds like a good plan. Honey also might help. (Good quality organic wild honey) It has good healing properties, and would be harmless if licked. The thing is to massage in whatever you choose to use, and do it as long as you can without him licking it off. Hold his chin under the jaw, to kind of immobilize his licking, while you massage it in as long as you can.
Hopefully someone will know about something else to use.