I had to self diagnose and treat this myself on my 7 week daughter. One doctor and health visitor just suggested we put up with a weeping and leaking red lump on our daughters belly button. But I got really tired of it making a mess of her clothes!!
So the treatment is.... table salt! We applied it 2 times and it fixed the thing within 24hrs. Now her belly button is healthy and normal. I recommend using table salt to anyone whose LO has the same problem.