During the end of my opponents turn, am I able to use my creatures tapped ability?
Do these work like instants in that regard?
Yes activated abilities can be used anytime you could use an instant.
112.3b Activated abilities have a cost and an effect. They are written as "[Cost]: [Effect.] [Activation instructions (if any).]" A player may activate such an ability whenever he or she has priority. Doing so puts it on the stack, where it remains until it's countered, it resolves, or it otherwise leaves the stack. See rule 602, "Activating Activated Abilities."
RESOLVED
***as long as your creature isn't affected by summoning sickness