An interesting outpost, as so much can go wrong in the mirror. The reflection in the mirror physically and psychologically is the foundation of personal and social identity. The sense of self is gained in front of the mirror in connection with the gaze of the other in social interaction.
The mirror itself is of significance. I remember when I lived with a mirror nearby my bed it was horrible to see myself as soon as I woke up each day. Of course, the mirror is a reverse image so it is not as one appears exactly to others as most people are not completely symmetrical.
Selfies have also become the new mirrors even though they can be played around with. We live in a world of images and one can love or loath oneself. Identity problems arise in conjunction with such images, including eating disorders, body dysmorphic disorder and gender identity problems.
The psychological aspects of self and the perception of self by others is the foundation of relationships and so many developmental and psychiatric issues. Autism is interesting as it is like a soliptist bubble in some ways.
I have read some of Sartre's writing on self, body and otherness, which I found helpful. Also, the social sciences shed light on the issues, including Erving Goffman's sociological work, 'The Presentation of Self in Everyday Life'. Also, object-relations theory, especially the work of Melanie Klein, looks at developmental aspects of self identity, with the role of mother as the initial mirror.
One book which I came across which I see as very significant is Martin Buber's 'I and Thou'. It compares the relationship between self and a personal 'God' and the human other. This is of importance in imagination and fantasy. As belief in God is facing there may be more attention to the opinions of others for a sense of self and self esteem.
But, as for the solution to the problem of self loathing or excessive self-love I am not sure that there is a complete solution. In practical terms, ito throw away the mirrors entirely might result in a complete disheveled appearance. Also, opinions of others may be overvalued but do need to be taken into account for coping in social life.
I am an existentialist outsider in many respects but don't wish to be a complete isolate. As people spend more time on the internet and phones there is a danger of going into a fantasy life in which the other becomes more remote. It may be a way of getting lost in a life of fantasy and preoccupation with an idealised imaginary image of oneself. To find the balance in navigating self and aloneness may be the way to wisdom. Through feedback from others we gain some awareness of our own blindspots, which may be uncomfortable but essential for deepening self-awareness.