A basic CRB check only shows actual convictions and cautions. So your arrest would not show up.
However, an enhanced CRB check also shows any additional information that the police (or other relevant agencies, such as the Department for Children, Schools and Families) deems to be relevant.
Following the Soham murders, senior police officers have come under considerable pressure to ensure that all accusations of sexual misconduct appear in enhanced CRB checks. (Ian Huntley had been accused of sexual misconduct on several occasions but this did not appear on his enhanced CRB check). While this is understandable, it means that many perfectly innocent people are at risk of having their careers ruined. (When I was teaching, many years ago, a 14-year-old girl told me that she was going to find a way to be alone with me somewhere, so that she could falsely accuse me of molesting her. She never did so but the memory of this means that I know that some teenagers really are prepared to make false allegations).
If the charges against you were dropped because the police realised that the girl was lying, there's no reason why the police would regard the matter as 'relevant' in relation to an enhanced CRB check. However, if they were only dropped because of a lack of evidence of your (non-existent) guilt, rather than because of proof of your innocence, you're regrettably in the same position that Ian Huntley was when he applied to work alongside children. That means that the accusations against you will appear in an enhanced CRB check.
If you're considering a career path working with (or alongside) children or vulnerable adults it might be worth considering engaging the services of a solicitor to probe the police for an indication of what they'd include in an enhanced CRB check. (You could, of course, try to do this yourself but the police would probably exercise greater caution if they thought that they