The ringing in your ears may be a symptom of the concussion. It also may go away.

If I were you, and I hadn't had any cognitive problems in over six months, I would definitely try to see what I could do. (I've tried to see what I could do despite having cognitive problems!)

Instead of going for a jog, which does sound very nice, why don't you see what a long walk or a brisk walk would do? Or a short hike? Or something not quite as jarring as a serious jog? Then build up to a jog after you can take a brisk walk, or whatever, every day, or every other day, for two weeks without having symptoms return.