You should but if not the hospital will have one on call to see baby at hospital. I have a pediatrician for my kids now and she doesn't have privilege at the hospital I'll be delivering. So I'll be using the on call pediatrician.
At the hospital I was at, they had pediatricians that came in and you could make your follow up appointment with them if you liked them. I would recommend finding one before though, because I ended up not liking the pediatrician then all of the good pediatricians ended up not accepting new patients until April.
yes, it would be a good idea to start researching and asking around for ones in your area. they visit your baby in the hospital to make sure everything is good to go.
Most pediatricians are supposed to visit the baby in the hospital and check them before you go home. It's a good idea to have one picked out before your baby is born.