It's not clear what point you are at in college or the application process. My recommendation is that you continue to try to get the charge minimized or overturned. If it does stay on your record, then, you'll need to explain it without blaming the professor and by admitting that you realize you made a mistake by not reading the rules (at least). My opinion is that if you are not suspended from school or given an F in the class, this probably wouldn't be a deal-breaker for med schools.
I question the teachers definition of academic dishonesty. Academic dishonesty is a form of cheating. A university setting is designed to promote creativity, application of knowledge, and achievement. Looking to a teacher for what sounds like some direction in getting help for an assigned project may not actually be academic dishonesty. Cheating on a test is a lot different than asking a faculty member for help, regardless of instruction or circumstance. You did nothing wrong. And do not state you did something wrong unless you think you really did. And you didn't.
Nobody asks a teacher for help if there is an intent to be dishonest. You were trying to do an assignment with enthusiasm and are being punished for your enthusiasm and love of learning and achieving.
In the event that your future career would be adversely affected by this individual's misguided misrepresentations of your character, I would most certainly recommend legal counsel...but I doubt it would come to that.
So what to do? hard to know at which point to jump in at. You could wait it out and see if anything comes of this. ( It might not- no impact). You could take it up with a University Ombudsman for opinion. You could, if affecting your permanent record, especially beyond a grade, follow a formal grievance procedure based on your otherwise clean record and, as outlined above, above board motivations.
Should you talk directly to the offending teacher? Perhaps. That's a hard call. It would be nice if you could. You could meet, with the goal being to get out of the door with another, perhaps more difficult indvidual assignment and a handshake. realize you cannot truly control his response, but you are laying the groundwork for a documented effort at resolution so the onus is on him to deny you the opportunity to make good on what was a simple misunderstanding.
I wouldn't take this type of crap, as you are presenting it, lying down though. But I think the best solution is to try and resolve with the direct accusing professor and offer up double work, a few hail mary's, and a few lashes, suck it up and move on. I'd make it clear that you politely disagree with a labeling of your character as dishonest in a way that might be unintentionally defaming. He'll get what you are saying, I assure you....if you get what I am saying.
