"Big Brother Complex" is a problematic term due to usage of "complex" in some circles to refer to someone who idolizes (not necessarily romantically) the figure in question (their brother
). All of these tropes can also apply to a big sister
The trope you're looking for could be any one of these:
Other tropes that may be what you were thinking of:
If you want to help, check the trope links to Big Brother Complex
and change them to the correct page. It would be appreciated.