Im sorry to hear about your symptoms.
Well by far the most common cause of bleeding from the belly button is an infection. Your doctors are most likely right in considering this an infection. The presence of pus from the belly button also lends more credence to this diagnosis. Now as to why the antibiotics aren't working, well there can be a couple of reasons for that,
1) The first one is that the bacteria which are infecting this region of the body are resistant to the antibiotic which you are currently on. This is a very common cause for antibiotics not eliminating the infection. The best way to get the right antibiotic is to get a culture of the blood and pus draining from the site. If a culture has been done previously and the current antibiotics which you are receiving are according to that culture, repeat the culture once again, sometimes the initial culture can miss some bacteria or there can be a superadded infection later on. I would advise a culture of the discharge as well as specifically looking for hard to treat bacteria such as MRSA. MRSA is a resistant bug which requires special antibiotics to be treated with.
2) The second cause of this could be that this is not a bacterial infection at all but a fungal infection. This would explain the ineffectiveness of the antibiotics to clear up the infection. If this is the case you should ask your doctors to do a fungal culture of the discharge and maybe even add an antifungal to the treatment regimen.
Lastly, an abdominal ultrasound or CT scan wouldn't show anything if the infection is limited to the skin and soft tissue. An ultrasound can ick up on an abscess in the abdominal wall but if didn't that means its not present. One last possibility is that in rare cases this can be due to remnants of the urachal cyst which is present during development in the womb. That can be checked with the help of specialized tests to see if there is a pathway leading from inside the belly button. But as i said this is a rare cause of bleeding. I would advise that you first have your doctors look into the above possibilities.
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