My 10 year old daughter is going through a difficult time at the moment thinking that she is overweight and that nobody loves her, she has cut her own fringe off twice and has now got hold of my razor and shaved her eyebrows off, I am so worried that her behavior is a warning sign of self harm.
What you've listed are 3 symptoms of excessive obsession with self-image... thinking she's overweight, nobody loves her (probably b/c of her perceived appearance), and then being actively destructive to her visible appearance. Because you have identified these symptoms as unrealistic, it is definitely best to seek the advice of a psychiatrist as only they can evaluate the entirety of your child's state and recommend a balanced approach.
As some background: my child had some issues which I found concerning and upon taking her to a therapist, she was diagnosed with some issues which the Dr recommended some treatments for, including dietary and sleeping changes, therapy, and medication. My daughter is now doing much better.
Two additional points: 1) If the Dr wants to just throw meds at your child, seek a second opinion; and 2) in the "worst" case scenario, seeking professional advice which results in a "don't worry" diagnosis causes no harm but will give you comfort.
I wish you and your daughter all the best!