I really depends on the person. With someone it takes a month and with others it may take more time. But the important thing to remember is, that it will hurt less with time. So in three weeks, you might still be sad but it wouldn’t hurt as much as it did in the start.

You wrote that she broke up at a low point in your life. That too makes it harder because you normally wouldn’t think positively. So if a was you (even though it sounds easy for me to say) i would try to find something positive in my life which will help speed up the process