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Hi @raeger, welcome to our community!
I'm sorry to hear about your phone.
Was the battery replaced at an authorized service centre or did you replaced it on your own?
Based on your error description it does sounds like it's related to hardware rather than software since it goes from 100% to 0% in just 10 minutes.
Could you please try to charge the phone with another original charger, if you have an extra or if you can borrow one from a friend, colleague or family member.
If you experience the same behaviour when the phone has been charged with another original charger, I would reocmmend that you perform a software repair using Xperia Companion, just to make sure that this isn't caused by the software in the phone.
Let me know how it goes!
Thanks for the swift reply!
I agree with what @uliwooly recommended, the phone has to be inspected.
I'm afraid that I can only recommend getting in contact with your Local support team and they will be able to assist you with getting the device sent in and examined at an authorized service centre.
They can also help you with any question you may have regarding warranty, service routines and so forth.
Keep us updated!