I agree with Kitt, it is NOT a good idea to stay in the same house with your ex until he finds some place else to go. If you allow this, he may take advantage of you and take his sweet time getting out, which is just not a good (not to mention fair) situation for you. I also agree with Kitt that his staying there is a form of mental abuse. He is the one who decided to break up with you, it is your house, and he will have nothing to do with you, therefore it is his obligation to leave right away. He probably thinks that you won't force him to do any such thing, which is why you must be strong and tell him to get out. If he says he has no where to go, don't feel bad -- remember that he left you and put you into a situation that you don't deserve. If he doesn't have a friend he can stay with, give him a list of local hotels. Trust me, if you allow him to stay in your home this way it will only fuel your anxiety.
It is only natural that you're feeling anxious at a time like this, so please don't fear that you're going crazy. No doubt it will be a tough few weeks ahead having to deal with the breakup and its fallout, but you WILL get through it and your anxiety will diminish again. Just make sure you be your own advocate and tell your ex to leave so that you can work through the anxiety that much more quickly.