Underage drinking charge?

i was recently cited for underage prohibition under 21, open container, and littering. the situation was kinda crappy because i fact wasn't drinking out in public, but was merely handed an open can a beer right before three cops came over and busted us. i dont want to plead guilty to the charges, because i'm not, but i know i cant fight them because it would be my word against the cops and plus i live a lengthy distance from the place where it happened. my question is can i enter a plea of " no contest" in this case. i was reading about it online and it said that in some places that a plea of no contest isn't accepted. also i was wondering if the judge could possible take this type of plea as a way of "trying to get out of the charges" and give me a stiffer sentence. if anyone could help me out i would be grateful. oh and if it helps it happened in Columbus Ohio.