I had a similar rabies scare when I was bitten by a feral mama and her kittens trying to move them off the side of the highway and into a carrier where they wouldn't be squished.

First, take a deep breath.

If your dog had a rabies shot and the wounds are not deep enough to see a vet visit, your dog should be fine (though watch to make sure it doesn't start acting off).

As for you, you did the right thing by washing the wound. The biggest danger with cat scratches is Cat Scratch Fever, as rabies is unlikely (possible, but less than 98% chance) to transfer via a scratch and Feline Distemper is much different than Canine Distemper in that it cannot be transmitted to humans. Watch the wound, if it gets nasty put some antibiotic cream on it and if it doesn't get better, go back to the doctor.

If you freak yourself out and think you have rabies, your brain will begin imagining rabies symptoms. Instead of worrying about it, just remember. If the doctors had thought it was very likely that you had rabies, they would have strongly suggested that you get the shot and not just mentioned the price.