Only about 7% of rabies cases in the United States, occur in domestic animals such as dogs and cats. The risk of getting rabies from a cat is fairly low, with most cases of rabies now occurring in wild animals, such as raccoons, skunks, bats, and foxes. So your chances of contracting rabies in the manner that you described, is highly remote.
I would suggest that you consider seeing a therapist so that you can work on your fears/phobias, and be able to put your worries about rabies, to rest.
As always, the very best to you SGR!... Chuck