Took the team up off my back, like "That's not your jersey?"
To “put the team on your back” means to carry your team, or to pick up all the slack. In this case his “team” would be his friends, and he gave up on his friends for a while.
He could also be talking about being involved in gang violence, something hard to avoid on the south side of Chicago, and quitting that life, hence taking any kind of “jersey” off which would identify him with a gang.
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