it might be a better idea to bring your baby to your pediatrician rather than just normal GP.
Did you apply the antibiotic powder when baby was just born?
it helps to dry the umbilical cord, so it can falls off.
If still have pus now, you need to get it fix ASAP.
just afraid if too long there might be infection problem.
I am not sure though, did not mean to scare you, but if I were you, I'd bring my baby to paeditrician immediately.
Do not worry too much about the shape.
it's ok if it's big or small etc.
Everybody is different.