Check to see if your battery is holding a charge, if you have a volt ohm meter let the car run measure the voltage across the battery terminals check the voltage if 13.8+ your ok with the altenator. Shut of the car with the volt ohm meter still connected across the battery terminals if possible. Have someone turn on the headlights and wipers, battery voltage shouldn't drop below 12 volts which means the battery is holding it'* charge from the altenator. I the voltage drops below 12 volts down to 9, your battery is most likely the proplem.
Just because the altenator is charging the battery is needed to run other electronics, remember your car has an fuel pump, soleniods in the trans the list goes on and on, so the capacity of the battery is very important.