Please help give some ideas...

I have a 93 chevy lumina. It has about 90,000 miles on it and is in great shape- only thing every had to replace is the brakes (it was a grandparents care before I owned it). Just the other day my battery light came on when I was driving home... gave this info to hubby and the next night it was also on (ran fine whole time) later that night I was driving and my radio started to go crazy, and I shut it off, next clock went dead, dash lights started dimming, headlights started dimming ( this is on interstate) I made it home (about 15 minute drive from when it started) and barely made it up my driveway (felt like it had no power @ all). We replaced the battery- (it was a battery from 93). the car seems to be sluggish and the light is still on. I'm afraid it's going to die on me and I believe it may be the altenator??? Hubby says I should be able to drive it for a couple of days until we can take it somewhere... should I worry about it dying on me and can this drain the new battery?? Help :) Thanks!

Check the ground cable if ok, repl alternator, or the battery will be dead, you cannot drive like this!