Everyone, at every age, should have a regular doctor and at a minimum have regular check-ups. You pay your taxes, it is your right to have a regular doctor. Denying yourself a doctor's visit (the one you paid for when you paid your taxes) just for the sake of a "overburdened health care system" is not smart at all. Just because you are young doesn't mean you shouldn't maintain you health - and exercising your right to have health care. If you have regular checks, tests and follow-ups it will be way cheaper for the government to maintain you healthy rather than having to treat you after you get sick.
By the way, even if you only go to walk in clinics, they will swipe your health card and that will be a record of you being in Canada. If you do blood work or an X-Ray, they will swipe your health card and that also creates a record for you being here. I ordered my OHIP and it's all there.
By the way don't go to the clinic every week like you said before, that would be abuse. Find yourself a regular doctor (family doctor) and have check ups every year.