Self-overcoming/self-superation

Christine Christie'self-overcoming'

That is possible in the meaning "overcoming oneself", whatever that means.

Christine Christie'self-superation'

I had to look up "superation". It is archaic, meaning it is no longer used, and you will find it only in old writings.

I don't see any entry in dictionaries for "self-overcoming" Here are some entries of the prefix self + words beginning with "o"

self-obsessed
self-opening
self-optimization
self-ordained
self-organized

Words with self- beginning with "s"

Self-sacrifice
self-satisfying
self-secure
self-service
self-standing
self-starter
self-styled

Christine Christie

Do the words 'self-overcoming' or 'self-superation' exist in English?

'self-overcoming' sounds made-up, and I've never heard that other one nor do I know what it could mean.

A better plan would be to show us a sentence where you think these words might be used, and maybe we can let you know