Sprung in this case means being enthralled by a member of the opposite sex and under their spell or control. The idea that the season "Spring" is jealous of the fact lil Wayne has never succumbed to this is proposed for comedic purpose.
a tip drill is what they in the rap world call giving a stripper a dollar for her to rub on you, in this case the girl in question obviously has a large butt and an ugly face so Nelly is saying that shes not good for much more than grinding on him
Lil Wayne is saying he's in the way on the path to the top of the rap game, and you can't pass him. Aaron Brooks is the point guard for the Houston Rockets. Wayne is saying that he's dominant while making a reference to a point guard known for passing.
He is making a play on the expression "bottom of the map" (of modest, humble origins) by saying that he came from "the bottom of the trap." A "trap" is an area rampant with drug distribution. He was born and raised in a trap, so that's why he hustles.