It might be a cyst.
I just had one in my armpit that got infected and when cysts get infected, clearish-white pus comes out like you're describing.
But infected cysts hurt like a mofo, so it's probably just an ingrown hair.
Whenever something is draining or oozing like that, it's an infection. Keep it clean and don't wear deodorant so it doesn't get more irritated/infected.