Ahem ... a few things:
1. I know it sucks right now, but I really hope you'll share this story and I'd really like to know which side of the coin you were on. Someday you'll look back on this and laugh.
2. Convicted, pardoned by Obama, found not guilty by a jury of your peers, etc, it will come up in a background check. People think things like 'expunging' and only getting arrested but not charged/convicted won't come up ... everything does. Think about how easy it is to google someone and find out their life story. Now apply that concept to a statewide computer network that involves the police and courts.
Now, here is what AACOMAS states:
'list any misdemeanor/felony for which you were convicted or pleaded no contest.'
Since you're way past that point, it's kind of moot, and you have two options at this point:
1. Tell the schools now (before your interview/during your interview)
2. Tell the schools after you (theoretically) get accepted.
After acceptance and paying your fee, they will run a background check, and I don't care what anybody tells you about these checks (what's supposed to come up, what won't come up, etc) everything comes up in some capacity, there is just too much information out there and too many pieces in the progression of getting arrested/cited -> judgement.
It's your call whether or not you'd like to tell the schools before or after, but not saying anything and then trying to explain a prostitution charge after the fact probably isn't a good idea.
As you're well aware, this isn't a great thing. Keep in mind that you didn't kill anybody, you weren't selling drug to kids, etc, but medicine is filled with conservative, professional individuals, and this isn't something like a citation for drinking in the freshman dorms. My guess is that since it wouldn't necessarily affect getting a medical license/working in hospitals in your 3/4 years, it isn't technically a life-long blacklist. However, I would be prepared to do a few things:
1. Thoroughly and honestly explain what you were doing. Don't lie, don't pretend like it wasn't your fault, but show remorse, take responsibility, and let the adcoms know (when you do explain) that it was a lapse in judgement and you've grown up/will never do it again.
2. Be prepared to show them that you've taken steps to actually fixing the issue. Go to SA meetings (I'm not saying you have a problem, but you should be able to show the adcoms that you understand what you did and you're taking steps to correct it), talk to teenage kids in juvie, etc.
Finally ... and most important. Get a lawyer, tell them everything, and do what they say. I'm making a huge guess here, but I don't think this type of charge is the end of the world, so hopefully a good lawyer and a first time charge (let's hope) will make the consequences not too harsh and you can move past this.
Know that it's probably going to affect your chances, know that you're going to have some big explaining to do; be honest, own up to it, show it isn't a reflection of your character, and see what happens.
Good luck.