Look, if you really are 13 then I'm not going to give you the "drugs are bad" response, but I'm also not going to look at you like you're naive of the answer in any way. You'd know the difference between being addicted and not being addicted.
Firstly, if you use oxycodone for social anxiety and depression (and using it twice a week somehow helps you...I'm not sure how), you should stop using it for this purpose. You come from an upper middle class family? You need to go see a psychiatrist or at the very least explore alternate options. What you are doing is self-medicating. I don't doubt that you're depressed. Everyone at your age capable of coming on a forum like this to express what they're going through in a literate manner tends to be, tends to be intelligent and ahead of their peers, and unfortunately a long road of hardship often comes worst when you're that kind of person transitioning into an adult. Drug usage kind of comes with the territory. Doesn't mean that it should though. There are medications for depression and anxiety that will not carry this risk and will be far more effective. I'm not going to be a hypocrite and get angry at the choices you make with your life when I wouldn't to someone of age here, though the thing is that you are not finished developing yet. Your brain can't take addiction. It's not even a good idea you smoke weed or anything like that at your age.
I'll just give you the blunt answers:
Will you become addicted taking two 10mg per week? No, almost certainly not. Your tolerance will take a million years to go up. This however is done by absolutely nobody at all except for people recovering from pain who will soon stop taking the medication.
When do you increase the dosage? You don't. I didn't read through this entire thread but skimming through the third page, I have absolutely no idea how much you take now but I'm guessing it's considerably more as you've managed to aggravate people. I am however positive that it isn't enough for you to stop.
You don't have the willpower to stop? Yes you do. All you have to do is stop. Sounds stupid but it is and always has been the truth, for everyone without physical dependency that may kill them. Just stop. When I was 17 and I had enough, I flushed all my hydros down the toilet. That was that. If you do not take the initiative then due to your age, someone else will eventually and you might wind up in rehabilitation against your own will, stripped of your dignity.
Finally, if you cannot stop using an opioid, I would suggest looking into kratom, as it's legal, works and in general carries far less risk, is far easier to taper off at any given point in time. Taking a small amount of it may help you get through whatever withdrawals you are having (if you are having them) - it did for me - and in general it's just a good idea to get off the oxy.
Best of luck, only if you want it - saying this not to be harsh, it just seems there's been quite a bit of difficulty throughout this thread. I know there's a lot of disparity between all the condemning in this thread and what some are saying outside it to others about various drugs. Honestly kid, many of our lives are just fucked. The best drug is youth, childhood, that innocence of just being content at the slightest things. You think your depression is bad now, just wait until you're older. Don't waste the years of youth you have left like this.