You can go HERE and download 3Utools. It is a free program you can download to your computer. After downloading and opening the program, plug in your Iphone and it will detect it and give you information about your battery life. Also click on the link next to your battery life reading and it will give you detailed information about it...
You can get a quality replacement screen HERE on IFixit as well as the Battery.
If you discover that your battery is in need of replacing and you are pretty handy with a multi Meter, test your charging port (You can google how to do it) to make sure it is charging your battery correctly... you can clean out the port itself if it needs cleaned (It collects debris like a "Belly Button" Lol) and can prevent it from making good contact to properly charge the battery.
Lastly, there is an IC Chip on the Logic board called Tristar (U2) that can go bad (Especially if you use generic chargers instead of the original Apple charger) and can cause "Fake charging", Poor or slow charging and no charging at all. If that is the case, you can google the chip replacement repair and watch a few videos on the process and try to find a local (reputable) shop that does Micro-Soldering near you or even find one HERE on IFixit that you can Mail in your Iphone for repair. Most have a No Fix No Charge policy like I have and is relatively inexpensive.
Feel free to reach back out here for more information or just to leave a comment on what you did to repair your Iphone to help others in the community troubleshoot their similar issue :)