Don't worry you'll sort it out
Jagex ban me all the time for random stuff I didn't do, I genuinely send them an appeal full of junk that doesn't make sense and they unban me.
I think the appeals are actually read by a human but the ban system is automatic, so when you appeal regardless of what you type it brings it to the attention of someone who can see how retarded the ban robot has been.
I think a mod commented on it on a Q&A once.