climbing shoes

It sounds like either the shoes are not the right shape or fit, or there is a pressure point on your big toe. Or maybe you put too much weight on your big toe rather than spreading the weight across all of your toes?

Usually yes, but it should really be more of an uncomfortable feeling rather than actual pain. If you are used to climbing shoes, it may be fine, if not, you get used to it pretty quickly, assuming you didnt size down too much.