Welcome to 2CarPros.
Everything you mentioned indicates a battery going dead. Now, the problem is that where it was checked, chances are they don't know the alternator voltage is regulated by the power-train control module (PCM). There is a chance the alternator and battery that were replaced were good and the PCM isn't allowing the alternator to charge the battery.
With that I need you to do a simple test for me. First, I want you to charge the battery.
https://www.2carpros.com/articles/how-to-charge-your-car-battery
If you don't have a charger, remove the battery and take it to the parts store that sold it to you. Most likely they will charge it for you. This would also be a good time to have them load test the battery to confirm you didn't get a bad one.
Here is a link that shows how to remove and replace a battery:
https://www.2carpros.com/articles/how-to-replace-a-car-battery
Once the battery is fully charged and we confirm it is good, put it back into the vehicle.
Next, we need to use a volt meter. It is also referred to as a multi meter.
https://www.2carpros.com/articles/how-to-use-a-voltmeter
Once you have the volt meter, check the battery voltage with the engine off. It should be slightly over 12v. Next, start the engine and check the battery voltage. It should be around 14v. Let me know if it stays steady or if the voltages keep changing.
Here is a link that shows how to perform what I described above:
https://www.2carpros.com/articles/how-to-check-a-car-alternator
Let me know what you find. I will watch for your reply.
Take care,
Joe
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Sunday, September 15th, 2019 AT 4:53 PM