Can you post a photo? It would really help us give you better advice. Combs are so variable, and you haven't mentions which type it is. I do think that you need to clean out everything. You need one of the curved-tip syringes that are specifically for flushing wounds, and it sounds like the abscess (which it does sound like) needs to be opened and thoroughly flushed. Personally I would use hydrogen peroxide for an initial flush to get rid of all the pus and infectious gunk, then use diluted betadine (povidone iodine) for subsequent flushes.
You definitely want this to heal from the inside out, so keeping the wound open is important.