A wet and inflammed belly button. Why

Matilda is coming to 2 months old. We came to a specialist, recommend by Dr Wong. Basically, we noticed that Matilda's belly button is often damp and slightly inflammed. According to the doctor, there is still a little bit of the umbilical cord stump inside the belly button. So we were given a "magnesium stick" and cleaning solutions for 7 days' self treatment. It went away only after 12 days. Initially, Matilda was really uncomfortable. I think the "magnesium stick" burns. Heart ache lah. Like as if I am torturing my kid. But alls for the better. She recovered. Whew! Of course it cost a bomb!