Well if nothing else, at least I don't feel crazy any more....I have been experiencing these same exact issues. AND as many others have said, I used my beats for months before the issue developed. The irritation was the worst when I wore them on a plane (just a quick one hour flight). My ears were literally dripping all day long. I had to stand under the shower for at least 5 min just to get all of dried liquid off my ears and out of my hair.
I am working from home currently and would LOVE to use my beats again. I have tried cleaning them, putting vaseline on my ears before using them, and only using them for short periods of time, but nothing seems to help.
I hadn't called Apple because I thought it was just me but now I know that isn't the case. Even if I don't get a refund I will at least call them to add to the list of people with this issue.
I also am willing to provide any feedback if anyone gets someone on the phone willing to listen to all of us with this issue!