pumping after breastfeeding (FTM)

I want to exclusively breastfeed I really didn't want to use a bottle but it's been two days since my son has been born and my milk has already came in and I make more then he can eat he will eat outta one boob eatch feeding for 10 mins and he's full but then my boobs are still pouring out afterwards can I pump after each feeding and use the milk for when somebody else is watching him ? Also he takes a paci so if he can take a paci fine can I use a bottle and not have a problem with him latching to the breast