Well it's great that you have an understanding supervisor, that's worth a whole lot.

And technically you are under medical stress, so you aren't lying to your cubicle mate.

And if you're working from home for a couple hours before you come in, it's not like you're effing around watching TV or anything -- you're still being held accountable.

Don't feel like a fraud, you're not a fraud. You have a legitimate issue and you're dealing with it very responsibly. Your employers are actually lucky you're dealing with it in such a functional way. Just because you're not so dysfunctional outwardly doesn't make your issues any less legitimate or significant. You're trying to ultimately prevent things from being worse next time, right?