When mentioning a role in general, it’s often left lowercase:
A president is the head of affairs.
A governor’s responsibility is to govern.
He served on a panel of judges.
The administrators of the school are set to meet tomorrow.
When referring to a specific role or using it as an honorific or form of address, it’s capitalised:
Abraham Lincoln was the President of the United States.
I visited Governor Smith and Mayor Lee last week.
He served on the Panel of Judges.
That’s a very good idea, Administrator Paulsen.
In your examples, I would write:
“…when I was promoted to president of the club…” (generic title)
“From my experience as President of Pre-med Club…” (official title)