If anyone finds themselves in that situation, you should really apply to the court to have the records expunged. The record of the arrest will not go away just becuase the charges were dropped or even if you were found not guilty. However, if you were found not guilty or the charges were dropped, you should have the right, depending on where it occurred, to have all records relating to that event expunged. Those records could come back to haunt you in many ways, such as when you apply for a job. Being arrested and being found guilty of a crime are not the same thing, but most people don't see it that way and they will just assume you are of questionable character regardless of the final disposition of the case.
Of course, that does not change the fact that you were asked a more specific question on your application, "were you ever detained" that you did not answer truthfully. I think you will need to get advice from a competent immigration attorney to help you determine how to procede now.