Hi Rafe,
Going back to my first statement. When you ran in a straight line and received multiple m4 and sniper shots - you did not lose any HP. No FPS or lag can justify that, I also checked if you were desynced before I banned you - you were not therefore I do not believe a single thing here.
As for the screenshots, let's be a little realistic. You took screenshots of your folder confirming you didn't use hacks 2 hours before you got banned? It just doesn't happen.
A simple way for you to come back to the server would be admitting your mistake and uninstalling whatever you had used and never use it again, it's up to you how you decide to go with this.