I would like to know what the difference is, if any exists, between the expressions
Look within yourself
Look at yourself
Don't both refer to using introspection to find out what you think your qualities are?
Look at yourself focuses primarily on physical appearance. For example:
Have you looked at yourself in the mirror lately? You look terrible!
Look within yourself focuses primarily on non-physical/intangible qualities or characteristics. For example:
Can you look within yourself to find the courage to continue?
Using these phrases in the opposite contexts sounds strange and unusual to me.
Do note that there are some intangible qualities that can be inferred from physical appearance. For example, someone who is drunk and has vomited on themselves is probably irresponsible. So look at yourself could be used to refer to physical appearance, but that reference is further used to speak about intangible qualities.
Look at yourself! You're a mess! You're so irresponsible!