I think that you may have resigned from your company, but not yet left. When you have to break your side of an agreement in order to have a life then maybe it's time to leave. I'd suggest that you look for pastures new, quickly, before you are "sussed". Best of luck.
Piltdown
(For what it's worth, I have never pulled a sickie - but I've left jobs when the fun bit started being rationed by foul brained beancounters and human remains types)