I am without exaggeration an order of magnitude more productive in my life and in my work because of proper task management. And because I use a comprehensive system like GTD, I typically don't let things slip through the cracks either. Beyond testimonials, the psychology is pretty clear: the human mind is not built to efficiently keep track of responsibilities and commitments in a way that keeps us maximally productive. Externalizing parts of that system have clear psychological benefit.

But your own issue sounds like it is more rooted in procrastination. "The NOW habit" by Niel Fiore might help you out.