Welcome to the forums. Like you, I grew up in a competitive environment. Also like you, I do art for relaxation. I want to address both these points and I hope it gives you something to think about.
Firstly, a competitive environment will come with its stresses. Adding to that, you're also dealing with changes to your family life and the feeling that everyone around you is too busy to give you any time (a sense of isolation). That's a lot to deal with, and you're perfectly justified in feeling the way you do. It's not a sign of weakness.
Because you've been brought up in a competitive environment, you tend to compare yourself with the people around you. That's why you ask questions like "why is my stress more obvious than those around me". It may seem to you like you're struggling compared to others, but in reality, they may be keeping their emotions bottled up inside, which is far worse in the long run than letting it out. So don't compare yourself with others. Your responsibility is first and foremost to yourself, and if that means seeking treatment for the stresses, do it without regard for what other people will think. The school counsellor is a good start, and if you could bring yourself to speak to him or her about this, it would help because he/she would be familiar with what your school life entails. If speaking is hard, perhaps try writing a letter to the counsellor and handing it to him/her.
I'm happy you have drawing as a relaxing activity you can do with your time. But I wonder if you actually put too much thought into the activity such that it becomes, as TonyWK says, "an activity" (that is, an activity you actually put effort and through into rather than one that actually relaxes you). Art is relaxing when you don't put any pressure on yourself to produce, when you're willing to let your art fail and still don't feel like you've messed up. For instance, doodling is relaxing because you don't really think about what you're drawing. From what you say, it sounds like you're actually feeling the pressure from being restricted, and that means that drawing itself is adding to your stresses. Alternatively, I wonder if you'd be interested in exploring zentangles or mandalas - they're often seen as meditative drawing techniques. I've tried them both and find that drawing repetitive patterns does feel more relaxing than regular drawing.