Bad battery or something else?

I recently had my alternator die and ended up getting it fixed. Getting it
back from the shop, they told me my battery was on it's last leg and could
die any time now. I figured maybe if I'm lucky I could make it work for three
weeks at least.

It's been a week as of today. Went to start my car and with some slight
hesitation it turned. The battery light came on and my speedometer and
rpm gauge don't work at all. I can rev it up, but they don't go up. The car
doesn't die though. I'm too nervous to drive it, but I tried to put in reverse
and drive and it would move. The headlights don't flicker or dim. The radio
is all garbled and the engine is making a slightly louder noise as if it's
working harder. Could this still be my battery or something else? Everything
in me says it's the battery.