This sounds like a dying battery! Given the age of your system you likely need a new battery.
To prove this install this gem of an app! [https://www.coconut-flavour.com/coconutbattery/|CoconutBattery] take a snapshot of the apps main window and post it here for us to see [guide|21499]. It may take a few attempts to get it to run long enough to capture the info hopefully you can transfer it to another system to post here.
Here's the needed part [product|IF108-063] and here's the guide to put it in [guide|6306]
FYI - I'm on my fifth battery on my 2011 15" MacBook Pro!