I'm 15 years old. I have a really strong and high-pitched voice. I like songs and dancing too much but I haven't ever tried to sing. 4 months ago I tried to sing and saw that I have a good voice. At this time I tried to make high notes and I succeeded without practicing or knowing the basics of singing. At that time I hadn't felt any pain in my vocal cords or larynx so I continued trying to sing. Once while I was trying to sing I began to feel pain. Then I stopped till the pain had gone but now every time I try I feel pain in my right ear and the right side of the larynx. How can I cure this problem? I know I should have gone to learn singing but my family won't allow me to!
You think you sing okay when you tried it so you continued. This is good, it means you have confidence in your voice. But singing is a delicate art form that takes a lot of training to do correctly. I study with a classical vocal coach and I'm always surprised at just how little I understand about the inside of my body after lessons.
PAIN = INJURY, almost always.
If your throat hurts as a result of singing then you do not know correct posture, core breath, etc. If you keep pushing your voice without training you will damage yourself, maybe permanently, possibly developing cysts on your vocal chords etc.
You need to find a way to get to a vocal coach. At your age, is it possible to learn at your high school? If you go to a school with standard arts programs you may be able to join the school choir as an after school activity, or even for elective credit. Then, hopefully, you will get some training from a music teacher.
In my opinion, proper training is the only "cure" right now.
I've got an idea:
GO TO A DOCTOR
The most pressing issue here is the pain. Pain here is likely indicative of some form of injury, and definitely beyond the capacity of SE to respond to specifically. You should probably refrain from singing until you get that looked at by professionals.
In terms of singing, if your family won't let you get lessons, then that's okay. It's possible to teach oneself to sing, but my concern there would be technique. With improper technique, one can easily reinjure oneself or worse. The optimal solution would be to somehow get a qualified person to teach you to sing with proper technique. I don't mean that the singing itself is poor, I mean that the method of production of sound may be the issue.