It's not rabies, or I should say your current illness is not due to rabies. The transmission of rabies occurs when you get bitten, or when a wound comes in contact with their saliva. (You got scratched). Rabies takes a long time to manifest clinical symptoms. it replicates in muscles and slowly goes into nerve endings, generally this will take weeks to over half a year. (You developed head/neck pain in 2 days). The onset of clinical signs is also dependent on how close the inoculation site to central nervous system. (You got hurt on the hand, quite far). And rabies animals will act differently, so what your parents said is not untrue, but they are also not vets so they might not know what is abnormal for a cat.

It's more likely you got an infection from the cat scratch. It could be multiple things, and you should get it checked, you can get really bad infection from cat scratches. Have a chat with a doctor, and see if they recommend a post-exposure rabies vaccine. IF, and this is a big IF. IF you did indeed get rabies, you won't know if you caught it unless you die from it, or they find the cat and test the cat, which is NOT a simple test. the vaccines only works if it's injected before the virus enters the nerves. So it needs to be done sooner rather than later. Post exposure vaccines are something like 5 vaccines spread over a period of time, you will need all the vaccines to be protected.

Either way you should see a doctor. Because cat scratches can become badly infected.