Chris, one thing that comes to mind is that maybe you're trying too hard, and thus, you're using too much pressure, bad angle, etc. And I can see where it makes you angry so then you try even HARDER to get that sucker shaved...which probably makes it worse.

Leave your chin alone for 2 days (if you can get away with that, maybe do it on the weekend), and then take it easy--lighter strokes, always conscious of the right angle.)

For now, keep your chin moistened with Thayers Medicated or similar so that it will heal.

Good luck!