Here's proof CC Sabathia gave EVERYTHING he had to try to get the Yankees another World Series title ...
TMZ Sports got the former MLB ace out in NYC on Tuesday ... and he was sporting a bulky brace on his pitching arm.
When we spoke to sources close to the 39-year-old, they told us he needed surgery last week to clean up the mess he made in his left arm after pitching for the Yanks against Houston in the ALCS.
Tough dude, right?!
Of course, CC battled a TON of injuries in his last year in pinstripes .