Hi Carlos,
When we use "in my case", you are referring to something that describes your situation.
Example:
There was mass looting in my neighbourhood last year. Fortunately, in my case, I only woke up to a stolen bike.
We do not usually use "in my instance" in English to refer to something that describes our situation. Instead, we use "for instance" often to refer to an example.
Example:
For instance, a square is a four-sided figure.
Hope this helps
Lance