I got my belly button pierced about a week ago and everything was doing just fine. The plasma and everything was coming out and what not. Then I got a little sick over the weekend (about 4 days after getting it pierced) and now it's like really swollen and tender. It got to where I can barely pull the bar through to clean it. And like now the top ball is like almost sinking into my stomach? I went to the place where I got it pierced and he said to ice it and take ibuprofen to get the swelling down but that everything else looks fine. But I'm worried that something is wrong and I don't want it to like pull through. But everything says not to use neosporin or hydrogen peroxide. So what should I do?

You either go to a doctor or you stop wearing it. You could be allergic to the metal or infected. Infections are no fun. I had one that started at a bug bite, spread over my entire leg from top to bottom, and despite 2 courses of antibiotics, have residual problems months later, sort of a permanent arthritis/fasciitis that doctors just shrug at and say 'that can happen.'

What kind of metal is the jewelry? Did the piercer recommend using a sea salt solution?
The problem with navel piercings are that they are the piercing that takes the longest to heal and is more prone to rejection. Healing time for a navel can range from 6 months to a full year. Yes, it will be sore for a while. Make sure to do a sea salt soak for a couple minutes, 2 or 3 times a day. When cleaning it, make sure you are using antibacterial hand soap. Wash AND rinse all the soap out or you will get an infection. The sea salt mix should be about a pinch of sea salt (not epsom or table salt) to a shot glass of warm water. Make sure it is mixed and just soak the glass over your navel.
Also, never take the jewelry out if there is an infection unless the metal isn't either surgical grade steel or titanium. Doing so will trap any infection inside and make the healing that much harder.