You already have your own problems, so don't worry about me.

I would say it this way: "You have your own problems, so don't worry about me as well." Or, "You have enough problems of your own, so don't worry about me as well." I just made a few minor changes to the wording. Good job!

The conjunction doesn't sound right. Maybe you could write this. You've got your own problems already. So, don't worry about me (at all).