If you want to get a ticket dismissed, the best way to do so is to hire an attorney who can help you fight it. An attorney could explain the charge that you are facing, the way the law of possession works, the long-term impact of a ticket, and the possible costs and benefits of pleading to a ticket.
You don't have to be anywhere near the item in question in order to be charged with possession of the item. It was in your room, your room is "within your control," therefore you have possession of items in your room. An alibi defense is not a valid defense in this instance, but the fact that there were others in the house that night might be helpful.
Pleading no contest is, for your purposes, the same as pleading guilty. You will end up having to pay the ticket and you will have the citation on your record.
I have seen District Attorneys threaten to elevate citations to criminal offenses when defendants try to challenge the charge in court. Know that you risk a criminal charge if you try to take this to a trial.
I would strongly recommend speaking to an attorney about your case.
Best of luck.