Sweetheart, you are probably not going to like this advice lol.
(I am in the process of becoming a peircer )
As for what it could be, its very hard to say. I'm of the mind though that is probably scar tissue that has built up from the peircing. It could have been done wrong/crooked or just didn't heal because you took them out repeatedly.

If your holes are still draining, it is actually really important that you leave the jewelery IN rather than out until the infection is gone. The reason for this is if you take the jewelery out when infected, what can happen is the outside of the holes on either side will heal first, trapping any infection in, and has a good chance of actually causing scar tissue to build up and giving you a lump inside the nipple. This can cause problems later on.

However. I would ask your doctor because without taking a look at the nipple and what is coming out of it I can't really say for sure what that is, and if it is something problematic, it might be best to keep the jewelry out. You might also want to contact a reputable peircer in the area to have a look at it. But i know in my training that we are ALWAYS told to absolutely leave the jewelery in until the infection clears unless absolutely necessary.

What i reccomend though is picking up some Sea Salt... NOT regular salt unless you ABSOLUTELY have to, because regular salt contains Iodine which can irritate. DON'T use alchohol, or anything containing it as it will dry the area to the point of irritation and it really is not that great for clearing infection either. I suppose you could also use polysporin, but thats not usually reccomended either. The best thing you can do is 3-5 5-10min sea salt soaks per day. This will draw up any pus, infection, or blood that might be in the holes, and will help it heal.

Let me know if there is anything else I can help with and I will see what I can find out.