Bad alternator or bad battery?

I have a 1998 Honda civic, a few weeks ago I replaced the battery in it, it was over 10 years old and always needed to be jumped. Okay so two weeks ago I replaced the alternator in it. It was bad also. Car drove great. Two days ago the battery light came on, but I just ignored it. (I know stupid) Car still drove ok though. Yesterday my gages were jumping everywhere but I still made it to where I needed to go. TODAY I started it, lights were super dim, but I made it about 5 miles down the road and it died. Jump started it, drove it about a mile, slowly lost power, gages jumping everywhere and eventually steering locked up and car died again. Tested the battery it tested at 11 Volts so I left it on the side road. I'm a woman, not car savy and don't want to get ripped off, I have bought an alternator before for another car and it did this, went bad, gages were jumping everywhere and car would barely shift. Replaced the alternator, problem solved. That one however never left me on the side of the road. Any pointers would be great.

Testing, run the wire. Shake it down…

It is the alternator - the "battery" light is actually a warning that the charging system is not working.

The reason it ran for a while after the jump start is that having another vehicle's electrical system connected for a while put some charge in the battery.

Charge the battery fully and avoid running the car other than to take it for repair.

A normal car battery can only stand being completely flattened half a dozen times or so in it's life and if you keep running it down that will be wrecked as well.

It is most likely a bad coil sometimes they get corroded and cause problems like that.
Also check the connections on your battery terminals are tight also check the connection to your alternator is tight as well.
Loose battery terminals can cause the problem you described

It's the alternator. You ran the car off the battery when the alternator died until your battery died.

So you got a bad alternator, you can return it and get another one.

You were lucky to get a red light to show you the alternator was bad so you didn't have to get stuck, you don't always get a red light and you wind up stuck, that is why I like to have an amp meter in the car so you can always see if your alternator is still working.

You can test your alternator by taking off the battery terminal while it's running, if it's bad the car will stall, but just because the car doesn't stall doesn't mean it's not going bad, that is why gauges are nice to have, a volt meter and an amp meter in the car will tell you how good it's charging.