suggesting OP is a paranoid schizophrenic - or just with schizophrenic tendencies is a little offensive, no?
OP... test like UE says... if it really bothers them this much, they should be welcome.
Also, you have to look at your logic. You seem to be falling for some cognitive issues. Why would both sets of neighbors be interested in spying on you? Makes no sense. The odds of them both being youtube hackers, and spying on your is very, very low... even IF the first pair did.
you would be surprised how loud music can be depending on your environment. If my windows are open, and the door to the basement is closed (where my drum kit is) my neighbors can usually hear it to a degree. Either walking past my house or gardening on a quiet day. This stuff carries a long way, especially in quiet environments, so they probably are right. Obviously my drum kit is louder than your singing, but you get the picture.
You should try and be respectful, ask them times that would best suit them for you to practice, as you have a right to practice. But try and accommodate them. Also, ask them to test. If they are rational, this should be seen as a generous effort on your part and be more than willing to help.
If this type of thinking/sensations manifest often in your life and in various ways, then yes it is an issue worth persueing medically... but if it is an isolated event then I would not worry. You are especially at risk if you are a young adult, and even more so if someone else in your family has this illness, just FYI. IF you are getting close to middle age (~35+) the chance you are developing this disease is extremely low.Not saying you do... just seems like you are a little freaked out.