I'm not sure if there was a question in there, or simply a statement, but I will try to help anyway. Being a police officer myself, I can tell you that "detaining" someone is NOT an arrest. As you stated, simply being pulled over for a traffic violation is a detention. It is not an arrest. Someone is detained for the purposes of allowing the officer to continue their investigation. If he develops probable cause for the person's arrest, then they can be arrested, booked into jail, cited, released, etc. If no PC is obtained, then the person would/should be released as soon as possible. If you are never told that you are "under arrest", then you probably never were.
With that being said, if you were booked into jail, processed, posted bail, given a court date, the whole nine yards...definately sounds like an arrest to me. Now if the court later dismissed the charges, gave you deferred prosecution, or something other than that...then it is still an arrest. You just were never formally charged. Unless it was dismissed with prejudice, they can still re-file the charges until the statute of limitations expires. IF there was some fault or wrongdoing found on the part of the officers in question, and your detention and subsequent arrest was found to be unlawful, then I would agree somewhat...you were never arrested (technically), but in reality you still were.
Yet again, with that also being said, I don't believe it would be a good idea to hide this incident from schools. First of all, most applications that I filled out said that you must report any arrest/detention, whether formally charged with a crime or not, or even if the charges were filed and dismissed. I realize that many only say "arrest", which is our subject of discussion. I believe this probably to be meant as "arrest" in the general sense of the word, to include detention as a suspect. Secondly, if the charges were dropped because you were found to be uninvolved, then why hide it? If they find out later (which someone very well might), then even if you did nothing wrong, it appears as if you're trying to hide something.
If I were you, in the interest of full disclosure, I would report and briefly explain the incident. It avoids questions later if the incident were found by the school/bar assoc/employers, who check back to your law school app or other materials. A last word of advice...when explaining this incident to others, you might want to avoid calling the police "corrupt" unless you have evidence that they were. Saying that they made a mistake, or had errors in their investigation is fine. Saying that they are corrupt just screams of blaming someone else for YOUR mistake and/or saying that their mistake mitigates yours.
Good luck to you, and I hope that whatever happened, you learned from your mistake and have stopped whatever it is that got you in that situation in the first place. Anyone aspiring to enforce the law shouldn't break it...or associate with others who do.