yeah I have had that problem, except for me, my lip splits more on the lefthand side... I am suspicious that this is due to the fact that I use more pressure on that side for some reason.... I dont know.
It sounds like your problem with split lips is much worse than mine has ever been, but whenever I get that I just slather my lips with stuff right before I go to bed and the problem clears up in a few days. See your oral surgeon, and above all, dont freak out about it. You will no doubt be fine. This doesnt seem like a real career ending thing.