That is an excellent question and one that is best answered by your primary care doctor
or another medical professional who is able to obtain a complete history and perform a physical examination to assess what is the cause of this painful belly button symptoms that you are experiencing. In general, pain in the belly button is not normal and so it is concerning that you are having pain associated with this. Are you having swelling or discharge from your belly button which may suggest an infection or other pathologic process. Either way, a doctor will be best able to evaluate the cause of this and see how to treat you appropriately. With regards to your question, there are various ways to clean your belly button that do not require a lot of physical manipulation that may cause you pain. Other causes of pain could include rashes, shingles along that region, trauma or infection as mentioned previously. This is somewhat concerning so it should be evaluated by your primary care doctor in an urgent or semi-urgent manner. If there is an underlying infection, your doctor may consider antibiotic ointments or drops that could be placed within your belly button.