Hmmm. Yes, if you find the holes are already somewhat healed - you are abosolutely right it probably wouldn't be best to push the jewelery back through.
If it makes you feel better, it may LOOK like a wart, but I have never, in all my experience seen a wart on a nipple. I mean, anything is possible when it comes to warts, but i think it is highly unlikely. I even asked the owner of the shop I frequent and he has never seen anything like it either, and he has been in the game for 28 years

Thats not to say 100% it is not - I am not a peircer yet, nor am I a dermatologist who can say for sure. But i do think you can remain positive for now and try not to worry too too much.
I was thinking too that might be the case - in that the peircing was placed wrong. If you still get fluid leaking out of the nipple like that see your doc again, and if you get ANY major breast pain, swelling, redness or heat, see a doc right away because those are signs of mastitis, which can happen when the breast ducts and glands get infected.. and beleive me, its a very UNFUN thing to have. Painful and you get VERY sick like the worst flu ever. Im sure that wont happen though but its good to have worst case scenarios just in case.
For now if i were you just do the salt soaks. The salt soaks will help draw that fluid up and out, and at the very least, help it to heal without getting infected.
When you find out let me know.