Continue down the passage to a dead end with a save station nearby. From the looks of it, a cactus blocks your access to the Security Room. You may find the solution if you can contact someone with the ship's intercom. Head around the ship and back to the Rec Center. Stay cool as you run past crew quarters.
Orchids come out of each.
If you're fast, you can continue running and take the door on the left at the end of the hall. If you're not so quick, turn and fight, but leave yourself plenty of room. Either way, continue through the door on your left at the end of the hall. Manning calls as soon as you make it through the door. She's alive, but the transmission is barely audible.