Okay, here's the rewrite! While I'm not actively spoiling anything from Civil War, I would be wary of references that could be spoilers for anyone who hasn't watched the movie yet.
Steve's mind was a mess of pain. His vision was swimming and his muscles trembled with every movement he made. The holes in his leg and stomach leaked blood continuously. The soldier part of him—the part that he both loved and hated—told Steve to leave. To abandon ship and live to fight another day.
He told that part to shut up and continued to lift the massive piece of wreckage pinning his childhood friend to the floor. Around him, shards of metal and sparks rained down from the ceiling of the falling helicarrier. One beam landed worryingly close and Steve strained harder, pouring everything he could into lifting.
Bucky finally pulled himself out from under the beam and Steve let it drop, unable to move for a second as his muscles recovered. He still had the mind to look to Bucky, who was staring at him with that damnably cold gaze.
"You know me," Steve managed, willing Bucky to understand.
Bucky was going to attack and Steve stood to take it, but Bucky's cry of, "No I don't!" hurt far worse than the punch that sent Steve sprawling. He got up anyway. He had to keep getting up, no matter how many times Bucky knocked him down. Bucky was his friend—Steve couldn't stop. Not here, not when Bucky was right in front of him and in so much pain—
"Bucky," Steve said, "you've known me your whole life."
Another hit. Another fall.
"Your name…is James Buchanan Barnes."
"I'm not gonna fight you." Helmet and shield, gone. But Bucky was still looking at him with eyes so lost and angry that Steve wondered where the hell he'd gone wrong—"You're my friend."
Tackled. On his back—
"You're my mission."
A punch. Another.
"You. Are. My. Mission!"
More. His head was ringing. But—he was hesitating. Bucky was hesitating.
His brain didn't seem to be connecting properly with his mouth, but he knew that Bucky wouldn't forgive him for saying nothing at all. If I'm your mission...
"Then finish it, 'cause…I'm with you to the end of the line."
I know you're in there Bucky.
No more punches. A jolt knocked out the floor and then there was nothing but gravity and then something cold that swallowed Steve whole, and he thought, maybe it's best this way.
Then he thought nothing at all.