Poor logic. I've had pneumonia, does that make me capable of diagnosing another person with pneumonia? No. And just to be clear, OCD is described very generally for a reason, thats because it comes in all different shapes and forms.
And again, its actually 100% irrelevant because even if OP does contact apple, he doesn't even need to mention his sickness to get the phone replaced. Dealing with Apple is easy; send an email to the right person and it doesn't matter what your problem is, it will be taken care of.
And where did I mention buying a used iPhone? I specifically said sell his old phone AND take a loss; as in cover the difference between what he got back for his used, and what it costs for a new phone.
With all of the talk in the news and inter-webs, I know for me, if it smells like a fish, it probably is fishy. Posting fishy stuff in on-line forums tends to get the members irate. You get stuff like this: http://forums.imore.com/iphone-5s/274323-iphone-problems.html
The OP bought a brand spanking new phone, says it wasn't used for three weeks and then when finally used discovers the white color could send him to the hospital. It's not logical to me as when I bought my iphone 5s you couldn't pry the phone from my hands for 24 hours. However, I guess it's probable.
The bottom line is anyone who doesn't like their purchase after the exchange window has expired, should send an email to the office of the CEO, starting their position and ask for a phone exchange. Squeaky wheel always gets the grease.