My thoughts are it may not have to do with your sound system.

13.7 volts with the engine running is a bit low. Should be 14 volts or a bit higher. Why is it low? Could be something is taking too much current and the alternator can't keep up, or the alternator could be dying.

What is the battery voltage when the car is off (and has been sitting for a few hours)? Should the a bit over 12 volts. If not, your new battery may be bad.

First step would be to find out why the charging voltage is low. Might disconnect the power to your sound system and see if the voltage returns to above 14 volts. Otherwise, have your alternator tested.