How are rock climbing shoes supposed to fit?

I totally get what your feeling! The shows hurt so you assume you got the wrong size and are worried that you spent so much money on something that doesn't fit right! Ah, its good to know that your not the only one. With you first pair of shoes its natural for them to be uncomfortable, its a good thing the way you describe is a proper fit. As for the discomfort in time you will get used to the shoes they won't break in per say but they will become easier to move in to the point you don't notice them until you climb for long and then some pain will ensue.It will just take you some time to get used to it is all. Hope this helped!