I'm going to be honest here. From my experience, this has all the makings of a piercing horror story.
The rules about minors getting pierced are there for good reason. If your step-father does not have any legal guardianship over you, it is illegal for him to sign for you to get pierced. If he had legal proof of his guardianship, they should have been able to let him sign even with a different last name. The specific rules vary from state to state, so you will have to find the regulations for the state you live in.
I can't believe the piercing place told you to get a kit and do it yourself, that is medically dangerous. Those nose piercing guns are really bad in that they are very blunt and cause a huge amount of trauma to the nose cartilage. Also, I'm sure you didn't carry out your own piercing under what is medically called "clean technique."
Having just any old earring in your nose is bad, especially given the fact that you mention that you have to keep touching it constantly. If you don't wash your hands every single time before you touch the piercing, you risk contaminating it with germs you've picked up from everything else you've touched.
From everything you've said I would say there is almost a guarantee that you are going to have an infection in that piercing.
I suggest you read the following because if you keep moving along without info, you are going to have serious problems:
Nose Piercings Nose Piercings II, Healing and Aftercare Nose Piercing FAQ You need to get proper piercing jewelry with metal that are appropriate for healing a piercing and learn what it means to really keep a piercing clean.