Hi Engenious,
Indeed 'Je me suis fait cuire des oeufs' is 'I cooked myself some eggs'.
Without the context it is difficult to comment further but in French-
Cuire (to cook) is something that only food stuff can do.
Faire cuire is what the person does. (to cook something)
and Se faire cuire is to cook /make yourself something (to eat).
Hope this helps!