BATTERY LIGHT, CAR WONT STAY RUNNING

I HAVE A LEXUS GS300 1993, TODAY MY BATTERY LIGHT CAME ON AND MY CAR WOULD NOT START. I HAVE BEEN HAVING TO JUMP MY CAR OFF SO I BOUGHT A NEW BATTERY AND PUT IN IN. BUT BEFOR I DID , ON MY WAY TO WORK THE LIGHT STAYED ON AND THINGS KEPT FLASHING OFF AND ON. WHEN I SLOWED DOWN TO MAKE A TURN MY CAR DIED. THATS WHEN I REPLACED MY BATTERY BUT MY BATTERY LIGHT IS STILL ON AND THERE IS A SQUEAKING NOISE COMMING FROM MY ENGINE. I WORK LATE AND I AM NOT SURE IF I WILL MAKE IT HOME. CAN YOU TELL ME WHAT THE PROBLEM COULD BE?

THANKS