maybe it's an allergy to the metal also. is it hot to the touch...what color is the ooze?? if it's hot/warm to touch, really painful and pussing green lymph there's a good chance you have an infection, if it's just red, oozing, irritated feeling and almost scaly and your skin looks like it's trying to pull away from the jewellery it's probably an allergy. I'm only bringing this up because it would mean a different treatment then an infection. If it is an allergy you'd need to change the jewellery to a titanium or niobium stud most likely.
A whole other variable is how long are the studs in the jewellery?? If they are too long the piercings could just be aggravated because you haven't downsized your jewellery from the initial length designed to accomodate swelling. Maybe it is acting up because of an outside irritation (alcohol, compromised immune system).
If the redness and oozing comes and goes it's probably not an infection, it could be that you were too rough with it and tore the piercing and now the piercing needs to re-heal.
If your other piercing is fine it's probably not an allergy and a good thing to do would make a saline solution out of a quarter teaspoon of sea salt to 8 oz of water (hot as you can handle) and soak the piercing in that.
All things considered though I'm neither a piercer or a doctor nor have I seen your piercing so I can only speculate from my own experiences healing lots of piercings on my self.
For years I wore metal jewellery then one day it just started acting up, ears turned red and began oozing and got dry and scaly and felt irritated and sore, since then every piercing i've tried to heal with metal has given me nothing but problems so i said fuck it.