Nick Young Races to Hospital After Lakers Game ... Baby's On the Way!

Nick Young had a helluva night ... it started with beating the Houston Rockets -- and ended with BABY WATCH at an L.A. hospital.

Young's ex-girlfriend, Keonna Green -- who already has a 4-year-old with Young -- went into labor late Wednesday night ... so Swaggy P rushed to the hospital to try to be there for the delivery.

The good news -- Nick didn't miss the birth.

The bad news -- it hasn't happened yet and Young spent the entire night awake at the hospital.

We're told Nick's super excited and can't wait to meet his kid.