@goosefootba what you are describing sounds like a bad screen. This "a small purple blotch" would be a definite bad screen. Time to replace it and to see if that fixes it (yes, it will ;-)
Since iFixit does not yet have a specific guide for this, use something like [https://www.youtube.com/watch?v=ae0X79MYFvI|this video] to replace the screen. Replacements are readily available at many online stores.
While you work on your phone, take lots of pictures. Once you are done with it, take those pictures and create a guide for iFixit. That will help the next person that has a device with the same issues as you do. It's easy and fun to create these guides. https://ifixit.com/Guide/new The iFixit community will appreciate this.
Repair is War on Entropy!