It might be a hormonal issue so it's best to see your doctor about it.
I'm not sure if you know this, but laser treatment doesn't have a certain "minimum age" for when you can get it. I got my first round when I was only 15 and it worked great.
You can get it threaded or waxed professionally, but that can add up to quite a lot of money in the long run. In my opinion it's best to just get the laser hair removal because it lasts for years and you don't have to worry about going back every month for the rest of your life to get waxed or threaded.
I have the same problem as you, and I've tried waxing and threading. Threading made me break out like mad and it was honestly more embarrassing than having a hairy face. Plus it's painful as hell! Waxing was a bit better, I didn't break out very much at all. But the downside of waxing is that your skin is pulled and stretched all over the place and that'll lead to wrinkles and saggy skin at an earlier age.
Tweezers are probably best over shaving because when you shave hair tends to grow back twice as fast and thick and might make the issue worse for you in the long run and it can also leave stubble. I would recommend going to your doctor because you might have a condition which is caused by a higher than average amount of male hormone which would result in the hair growth around your face and other areas. If this is the case they will probably be able to give you more successful treatments that will prevent hair growth, I believe some of the medications are anti androgens like danazol.
If it isn't a medical condition there are other ways you could get rid of the unwanted hair, you can get hair removing creams which wouldn't leave stubble or there is electrolysis which removes the hair using an electric current (it's all very safe), however that can be expensive, not altogether practical and might not be recommended for someone of your age (I'm not sure). I'm sure there are some natural options you could try aswell. Try to drink more milk a day and maybe increase any dairy products you consume as anything with Calcium D vitamin can work to remove hormones.
Good luck and don't pay any attention to the ignorant people who are giving you a hard time :)