I got my lip pierced yesterday with a stud not a ring and on the inside of the ring there's a disc to obviously keep the bar in the lip and no pulling through.

It appears that my lip is forming around the disc, almost as if it is slowing growing into my lip. Is this just because it is still swollen or should I be concerned ?

Its most likely due to swelling since its such a recent piercing.

It might be wise to have a doctor examin it though, since we can't diagnose properly over the Internet. ;)