Try not be be so hard on yourself. It's just part of the process and that anger will spur you on some more in a positive way.
I did something very similar today when I contacted ex about a drop off time for our DD next week. Well the stupid fucker forgot, again, and then ended up calling me names because I pulled him up on it.
I replied to him with some home truths which of course he didn't like, and never will as he is a victim and has done no wrong.
The good thing was that I wasn't even bothered afterwards. A short time ago I would have beaten myself up about it but I think I'm feeling indifferent, most of the time now, which feels like a really good place to be.
I no longer intend to allow that emotional retard get me down anymore.
He has already stolen enough of my happiness.