I have replaced battery today and alternator a month ago. When I put in New battery it ran fine for about 10 min. Then the brake and battery light came back on. When I accelerate it goes off. What could cause this issue

 

The alternator probably failed again. Unfortunately re-built alternators can be hit or miss, especially the ones autozone sells.

Get your voltmeter and do some tests. With the car turned off, measure the voltage across the battery positive and negative terminals. A good battery will measure 12.3 - 12.5 volts if it is fully charged. But if the battery measures around 10 volts, then the battery may have a dead cell. Now start the car. Measure the voltage at the battery again. If the alternator is charging, the voltage should read 13.8 - 14.2 volts. If the voltage reading is the same as before starting the engine, the alternator is kaput.

 

If you do prove our that the alternator is bad, the one you put in might be under warranty.

If nit, I suggest having a local electrical shop rebuild it. Then you know for sure what's been done.