If my navel got pierced yesterday at a reputable shop and its only slightly sore today with no crusty things or anything associated with a piercing and the bar can be felt is it rejecting?

it is normal to be sore and have a slight red tone to the surface of the skin after a piercing. There are pain receptors and nerve endings where the piercing lies....as long as there is no pus, swelling and severe pain you should be fine. give it about 3 weeks for 100% healing time.