Once a case is dismissed, one still needs to seal the record assuming State Court to deem it never to have occurred on this state. Not sure who denied credit and for what basis, but generally, credit is not denied on dismissed charges. However, private businesses have a lot of latitude on who to lend and/or offer credit. You may have an action against the "person" and/or "persons" who lied (assuming they did) about the facts which eventually resulted in charges being filed.
The answer above is only based upon the limited information provided. The answer is limited and my review is likewise limited, and thus the response is not intended to be acted upon as legal advice. Although licensed in numerous states, I am currently only licensed to practice law in the state of Nevada. No attorney-client relationship is formed until you sign an attorney-client agreement with my office. Any information provided is for discussion purposes only and there is no attorney-client relationship formed. Only general legal information is provided. Each case is unique and accurate legal advise would require review of all details and documents for each specific case. It is possible that the comments here, while meant to be helpful, may in some cases not be complete or accurate.
George is right: get the arrest sealed by an attorney in the county where it occurred.
Second, remember that no one *owes* you credit, it is the lender's to offer on their own terms.
Clark County, NV practitioner.