Need some help

My phone is not doing good, I have an iPhone 12 firstly the back glass got cracked idk how I use a case at all times but it got cracked, I used a skin to cover it up now a couple of months later the screen is lifting from left side, i donno if it’s the battery or something because the side it’s lifting up from is not the side where the battery is, I had gone to a repair shop they quoted 3.7k for a original battery also the, I was thinking of replacing the battery as it’s really bad, 63% BH, and the screen where it’s lifting up, the pixels are damaging, can’t go for a new phone since I am a student, what should I do go for a back glass and battery replacement? I need some help to sought this out, original parts are good in price online from whole sellers should I buy it and go to a reapir should and tell them to just replace with the ones I bought?