Reticent means either quiet or restrained. If you're reticent about your feelings, you like to keep them to yourself, and you're probably quiet in rowdy groups where everyone is talking over each other.
The original meaning of reticent describes someone who doesn’t like to talk. Be careful in your context, however. Reticent can refer to someone who is restrained and formal, but it can also refer to someone who doesn’t want to draw attention to herself or who prefers seclusion to other people. Don’t confuse reticent with reluctant, which means unwilling.