Screen popped out 5c causing connectivity issues

Last week I dropped my iPhone 5c and the top left part of the screen popped out. I didn't think it was that big of a deal so I popped it back in place. Soon afterward, I noticed that my phone would show the wrong time even when I adjusted it myself. Bluetooth works sometimes but not often. The wifi keeps switching to LTE even when I'm connected to a strong network (like at home). iMessage randomly disables itself and I'm beginning to only receive calls and messages to my iPad but not on my phone. The phone is now starting to become useless and I don't have a warranty because I bought the phone refurbished. I perform a soft reset several times a day and even restored my iPhone to factory settings. I don't know if Apple can do anything for me since I dropped it and I don't have AppleCare.