I agree with this action.I would like to hear what others have to say, but if he were mine i would treat for worms with Safeguard liquid for goats, coccidiosis with Corid or Baycox, and a bacterial infection with Baytril.
@anniep you don't mention what type of feed you are using. If it's layer feed, go get a small bag of fresh chick starter or flock raiser, use that instead, he does not need the calcium in layer and might benefit from a little extra protein.
I would soak the feed in water for at least 30 minutes, give him wet feed. I like to give mine egg so that's great. The mineral oil, I would probably add that for a couple of days more too since the poop is so dry - it's coming out thin because of swelling and he must be straining too. Hopefully the wet feed will make it easier, he does need to be drinking well too.
As for caring for the prolapse, if it will not stay in, keep the exposed tissue moist. Most of the time a prolapse will not stay in until swelling has gone down, so this is not that surprising, but the tissue can die if not kept moist. Use your oil/ointment of choice for that - things that help retain moisture - honey, sugar pack, hemorrhoid cream/ointment, anti-inflammatory cream, vaseline, coconut/mineral oil, etc.
Soaking may help too, you can keep up with that. In between soaks if he's messy, a spray bottle with an epsom salt water solution to spritz him off may make it easier on you.
Keep him where flies can't get to that, you don't want to add them to the mix at all.