Wow you sound just like me when I was 16 (I'm 24 now). I have always had anxiety but when I hit 16 I got hit with anxiety, OCD, and depression full blown. I felt like I was going crazy. I was failing everything because I couldn't concentrate. I played video games too (I still do), and they can get quite addictive when you are using them to cope. You might want to tell your parents that at least they help you stay away from drugs and alcohol (if that's the case). You need to see your doctor as soon as possible and explain to him/her what's going on. I did this and she referred me to a psychologist and she also put me on a low dose of Prozac which made a huge difference in my life. In my opinion, anxiety medication is not something you want to stay on long term, but it helps you deal with the anxiety in the short term so that you can rationalize it and overcome it, while in the future, hopefully through counselling, you will learn skills to help you manage it. This is what you need a psychologist for, though sometimes a counsellor with a master's in social work is cheaper and can also help. Talk to your doctor and see what your options are.

I promise you things will get better though. I'm now in university and doing well, and I can manage my anxiety without medication. I still play video games but I am able to play less and only for fun rather than for coping. For now, you can focus on mindfulness: write your emotions down and observe them non-judgementally. Don't think of them as good or bad, just write them down, observe, and then let them go (if they are unpleasant). Try some light exercise, read a good fantasy book before bed, spend some time with a pet if you have one, or watch a favourite movie. These things will help you relax and fall asleep, whereas video games get your adrenaline pumping.

You don't need to be sent to a boarding school. Sit down with your parents and tell them frankly that you think you have an anxiety problem and you want to take steps to feel better. If they are really hard to talk to, you may want to talk to a doctor or counsellor first, who can then explain the nature of anxiety and depression to your parents. Good luck!