Don't half a pill w/o asking your pharmacist if they can be cut. Some meds are time released and when you cut them in half you get way too much medication. W/O knowing what you are taking, the general rule of thumb is two weeks of sleepiness on average until your body adjusts. I'd start out taking the minimum amount possible - that's my advice coming from years of working in the mental health field. Can't give you any personal based advice.
I am glad to hear that it wasn't your heart - whew!