Tiffany,
First off, regular table salt and sea salt are not the same. Sea salt does not have added chemicals or iodine, which might be adding to the irritation that you are getting.
If you get sick, especially if you blow your nose alot, that's going to add to the irritation.
When your nose is newly pierced, the tissues swell from the trauma and from the body bringing more blood to the area to try and help heal it. Wearing a stud can be hard, as they usually fit it based on the thickness of your nose before you get it pierced. Then when you get the actual piercing, you swell up. You need to either go back to the piercer and have them switch it to a stud with a longer post area for the part that goes in your nose, or you need to switch it to a ring.
Try taking a bit of supplemental Vitamin C and zinc to aid with the healing. Go as easy as you can on the nose as far as your cold and repeated nose blowing go. There's not much that can be done about that really.