I'm so sorry that this has happened to you.
I'm sure that most of us have been unjustly accused of something. I had one year when a single family leveled many false accusations my way. There was just enough fact in the stories that they were plausible. My principal stood behind me, but she did do some checking to make sure that her faith in me was justified.
I felt like quitting. I felt my reputation might be ruined. I wanted to quit. I cried an untold number of tears that year. BUT the next year was much, much better.
This is a long and twisted story that I've condensed into two short paragraphs for privacy's sake. These kind of things are usually long and twisted. I'm sure I don't have a clue as to all the things that motivated my poor little family.
I know you feel miserable now. Things will get better.