The screen on my iPhone acts weird

I had a battery replacement from a local repair shop an year ago. It was fine, until recently the phone heats up like crazy and got incredibly slow. Also the screen acts weird, it open apps, scrolls and toggle settings on its own and also fails to register my touch often. Also sometimes back the screen had vertical blue lines which doesn't show up anymore. Could this be solved by a battery replacement or is this because of damaged lcd?