Is she an only child, OP?
My daughter is the same. Very sensitive and takes everything to heart. I put it down to her being an only child.
When you have a sibling, you are exposed (almost daily!) to arguments or fights and wrongdoings and urges to 'tell on' someone. The parents will be likely fed up of it and will often say 'sort it yourselves'. The children therefore gain the skills to stick up for themselves, to negotiate, and to resolve upsetting issues at a faster rate than their only-child peers who aren't exposed to conflict so often.
That's my theory anyway! 
I came from a huge family. I was called names by my brothers every day and got into physical fights with my sister once every few weeks. My mum was fed up with our constant complaining about each other and never sorted arguments out for us. At the time, I resented her for it. But upon reflection, i see that her lack of interference actually helped me to conjure some amazing one-liners and a brilliant level of emotional resilience.
My advice would be:
Not to interfere when she is getting upset at small things e.g. going to the teacher about her being upset over kissing a book. Tell her why she should not be worried about this kind of thing and then move on. Don't dwell on it.
If she's upset about a silly name or something that someone has called her, ditto (unless, of course, it's persistent bullying). Don't go to the teacher on her behalf. Ask her what she thinks she should do in that situation. Maybe build her confidence to approach her teacher herself with the complaint, or give her a good comeback for future situations (one that won't get her into trouble).
If she does happen to have a sibling, stop interfering in their squabbles. Tell them to sort it out themselves.
Expose her to more situations where she can interact with peers to build her confidence and resilience. e.g. drama club, soft plays (these are great for developing resilience. She'll witness lots of wrongdoing and rule breaking, constant squabbles over the slides and 'he bumped into me!' complaints).
Feel free to completely ignore my advice of course. Reading it back, it does sound a tad awful. But it's what worked for my daughter.