The first game, I actually watched a team fight go down in front of me, while I was frantically mashing the heal button to save my allies, before I realized: "I should... probably be in there, killing them, instead," and then turned into a cougar and pounced in.
In the second game, my five-man decided to make me solo top against Sion and Garen, and it kind of went like this:
"This Sion and Garen are harassing me so hard. Boo hoo, me. "
"Hold me close, tower, you are my only friend. "
"I'm so lonely, none of my friends will come save me. "
"Oh, I'm level six. I'd better use my ult before someone on my team scolds me. "
"Huhn. I seem to have killed that Garen."
Everyone was surprised, but no one moreso than I.
So there are good games, and there are bad games. I still hang back a lot, healing, trapping, and throwing spears, but at least now, I throw spears for good damage, and get away from the fight handily with pounce. Soldiering on with Nidalee Experiment.