I've always had good results with lye soap...
The secret is to make the skin less oily.
Next time... Wash with soap immediately after exposure.... And you probably won't break out.
Re the rash you have now?
Agree with grow a beard.
The secret to healing faster... Is to stop irritating the rash.... If you can stop scratching, you don't actually need to treat the problem area(s). But... Yeah, shaving seems like just the thing to make the rash larger...