After Lara regains consciousness and the camera shows her hanging upside down in a scavenger. How can you gain control there?
Alternate pressing right and left and keep swinging until you reach the fire. When Lara touches the fire and ignites the cloths wrapped around the pole. Swing Lara with this file to burn until she drops to the cavern floor.
Dropping from up to the nasty spike, to remove the spike, tap the interact button (E on the keyboard, square on the PlayStation and X on the Xbox) repeatedly as shown in the Video.
Lara is now free but feeling not well her vision is blurred and she is moving Zigzag.  
Approach the TORCH on the wall and Press interact to take it. Walk continue along the tunnel until you reach the piles of flotsam. Stand close to the flotsam and hold the Interact button to burn the piles and clear the way to the next area. Continue walking through the tunnel.

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 Tomb Raider 2013 Part 02 Walkthrough

Complete the Walkthrough of Tomb Raider 2013 Part 02 in the below videos.