How long can I wait with drug abuse to see if it goes away without seeing a doctor?

Why wait? The point is that you don't have to do it alone. And it doesn't just go away like a cold. Get help and support at any 12 step meeting and get an evaluation by a psychiatrist. He may recommend only the 12 step program, or he may be able to help you even more!
Drug abuse. The longer you use any drug or alcohol, the more dependent you become and the harder it is to end your use. The question should be how soon can you stop, because the sooner the better. Call or visit an aa or na program, enroll in a drug treatment, get the help you need!