With respect, if the tooth were to be infected, it could potentially get dangerous as with any infection and be quite painful. You have no idea what the tooth looks like or how much pain they might be in. One week is a long time to wait for an appointment with a horrible toothache.
As for the infection spreading to your brain, this isn't going to happen. But if it's painful or seems to be getting worse don't wait a week, you don't deserve to go through that.
Also, be careful about repairing your tooth at home as you could definitely do more harm than good and trap any bacteria in the cavity.