Battery and Brake light

Yesterday I was driving to the store, my brake and
battery lights started flickering. After I drove about
a mile, they shut off. Coming home, they were
flickering again and the car lost acceleration.
It wouldn't go over 5 mph.
All of the dash lights came on, they were not dim.
AC still worked.
Power steering wouldn't work.
After a couple minutes, the car started driving
normally enough for me to make it home.
As I pulled into my complex, it did the same thing.
Before I could get it parked, it died completely and I
had to push it into a parking space. I tried to restart
it, it started to turn over but lost power.
Before I fork out funds for a tow truck and new
alternator, do y'all have any suggestions for what
else it could be?