A member on here, donnj, taught me a trick that I've used quite often the last few years:
With the car already running, disconnect the positive terminal on the battery. If the car continues to run, the alternator is OK. If the car dies, then you have an issue with your alternator.
My crude understanding can be condensed down to: "Battery just starts the car, alternator keeps it running."
In the meantime, charge your battery so you can get to an Advanced Auto or the like, and have your alternator tested for free. I once drove 52 miles to work on a fully charged battery, had a gas station mechanic charge it during my 8-9 hours at work, then drove the car 52 miles back home
(it was a Friday and I couldn't do the repair until Saturday
)--Point being, charge the battery as a temporary band-aid to get you to the nearest part's store that can test the battery, alternator and starter for you.