About removing negatives from report

Hello all,

I have about 12 negative accounts and 1 collection on my credit report :( My question is, though all these negative accounts have been paid in full including Collection then why are these showing up? How can I remove these items from my credit report? or are they to stay on their for 7 years?

I have a secured card too since 2009, which I am managing very well. I just asked the bank if I could change this to an unsecured one. They said I will have to wait 5 months. I also have 1 small installment Loan which I pay on time every month. Should this be enough to help me build a very good credit score??