Your credit score is most likely the thing that is holding you back. Keep in mind that your whole payment history is kept on your credit record. The combination of all your payments forms your credit score.
If you remove the adverse listings it will not immediately increase your credit score. Your payment history is still there, and it is going to take some time for your credit score to increase.
It is important that you wait about 6 months before applying for any credit. Everytime you apply for credit and you are declined it also negatively affects your credit score. You must be patient, allow some time to pass, and pull your credit report again in 6 months.
the payment history will remain there for 24 months… but generally your credit score starts to recover after about 6 months. Provided that you did not do anything to harm your credit score in the meanwhile.
Key here is to be patient and be informed about what is going on with your credit report.