It seemed SHIELD related to me, and I am pretty sure we are to assume that she's on a SHIELD mission. And so far we've seen her working for SHIELD in IM2, Avengers and TWS. It's safe to say she is fully SHIELD. Her Marvel wikia also mentions her as an agent of SHIELD. Nothing in the MCU so far has said otherwise. I doubt she's freelance. And yeah, Barton gave her a choice to either come over to SHIELD or die. She chose SHIELD.