The car won't start let alone keep running. The battery light was on for awhile but the car was running fine. Then I was driving and it just started sputtering and died and even when I jump it it only lasts like 20 seconds and starts sputtering and dies again.

First check to make sure you have a serpentine belt if you still have that then get your battery and alternator tested at an auto parts store

It sounds like you have a faulty charging system and could be the alternator itself, the regulator in the alternator or the diode stack. Have these checked. If a battery has reached the stage where it will no longer take a charge it would have the same effect, but have the alternator checked first before replacing the battery. (Does the engine keep running with the jump battery connected, if so, check if the jump battery is being charged while the engine is running, The battery voltage should read up to 14.5 volts at around 2000 RPM).

Get the battery & the alternator checked (Autozone, O'reilly's or even Pep Boys can do that for free). If the alternator is out or going out, it's not charging your battery - that means everything electrical in your car is now trying to run directly off the battery & draining it (it doesn't take long - especially if the lights or A/C is on). If those check out ok, take it into a mechanic & have them run a diagnostic - you may have a relay out. Good Luck.