Unhappy about one's appearance?
self-conscious, according to vocabulary.com
Being self-conscious goes beyond just being aware of yourself — when you're self-conscious, you constantly question the way you appear to others
Expanding on the OP's example:
Anne is very self-conscious about her hair. She is always trying new shampoos and conditioners and experimenting with new styles.
A person who is self-conscious about their weight may or may not be too heavy (or too thin) but they think they are.