Jennyjoan, if you don't want people round on your birthday, don't invite them. If they do come round, you will of course be your usual hospitable self and offer food and drink, but it doesn't have to be a big thing.
I would have thought that your cousin would be a bit more sensitive to your needs, but some people just aren't. Don't go again if you don't need to.
I'm not sure where you're going with the immaculate conception in your last paragraph, but obviously many things are bothering you. Try to relax for now.