Who = he/she or them.
I who = visualization of a group of two or more individuals where we are referring to a single person ( he/she).
We who = visualization of several groups of individuals where we are referring to a single group.
I who thinks = he/she thinks.
We who think = they think.

"Not just I/me who thinks..." is correct.
"Not just I/me whom thinks..." is also correct.

Whom is the formal way of saying who.

Example: To whom it may concern.

Think of math.

x+y=z

X represents an unknown number (same goes for "y" and "z").
Who represents an unknown person or persons other than ourselves.