Battery repair pricing. brand new instore, 6months old

Hi I’m wondering how much would a battery replacement be for my iPhone 8+? My husband just bought me this phone not even six months ago brand new from T-Mobile no contract. We have moved to another state system so there’s no way I could go back to that store. But during the first month I noticed that the phone would show a warning about the high temperature and that to let it cool down before use. So I thought maybe it was because of something else the battery never crossed my mind. And then I had bought a new case which was like a rubber Louis Vuitton plastic kind of case and when I switched to a different case that I had just bought I tried to take out the Louis Vuitton plastic case and before I could even take it off I could see the front screen listed above the side of the phone case so I gently took the case off and examined the lump and googled. I was told it’s a bad battery. Is there a warranty or something? At the moment my phone will not hold a charge at all unless I keep it connected to the charger and even while it’s on the charger it turns off and takes forever to turn back on. To have my phone working is the most important thing to me right now because I had my first Nuro appointment and many more doctors to see who were trying to get a hold of me and in the middle of our conversations my phone hangs up on them and then it takes hours to come back on while it’s on the charger so I’m just trying to get a rough estimate of what may be someone in the community has paid for like my device. I am taking the phone up to Best Buy if that info is needed I had to schedule an appointment for next Tuesday the 17th and it may or may not be fixed I will ask them and find out the total for the repair if I can’t get any insight on the price range here. Thank you in advance for any advice and support🙏🏼🦋

[Edited by Moderator]