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Tony in the Iron Man armour is easily worth two of any ordinary field agent, you decide, including you. So you opt to go with Hill and Sitwell, because they’re the team that’s going to need you the most, and you’re not having anyone go off to rescue Natasha without the best possible odds.
All S.H.I.E.L.D. agents receive a tracking chip embedded underneath their skin upon engaging field service status. This is why. Coulson issues the activation command remotely, and as soon as you and your new teammates have a lock on the signal, you plot a course across the compound in its direction, trying to figure out how to remain as unnoticed as possible for as long as possible.
There’s an isolated cell block in the far corner of the compound; it was empty when you arrived, and now you think you can guess why - it’s reserved for the ‘high-profile’ prisoners.
Natasha, evidently, is high-profile.