In my opinion, (and this is just for me, I can't speak for all) the hurt never really goes away. However, it does get better with time.
It's hard to let go when you've been with someone for quite some time, when you know how long that the person takes in the toilet, when you're used to having someone next to you on bed, when you are so used at his peculiar peccadilloes and habits that anyone else having the same traits will be immediately associated with him. Suddenly the bed feels too large, everything feels 'empty', and loneliness eats you up. Even though you may realize that its for the best, we can't bottle up all that has happened in the amount of time that we've been together and throw it away, never to feel it again.
We're all humans, with the ability to feel, to love, to hurt; and to feel pain, sadness, joy and laughter acutely. There will be times when a certain scent, or a place, will trigger off an onslaught of memories and emotions... and as long as the hurt is still fresh, it will assail you over and over again.
But we get through things... we move on, we learn to let go. Give yourself some time. These few months (or even years) will not be easy, but it will get better in time. It will stop hurting you the way it does now - and all that will be left, are just the memories of what used to be. Hopefully, when that happens, you can look back with a smile on all the good things that used to be - rather than how it's like now.
We never forget, and there will always be that 'twinge', but over time, it won't hurt as bad.