A story in which an aspiring physicist struggles to overcome self-doubt after her family tries to convince her that a girl cannot be a scientist is facing--

An internal conflict; the protagonist vs. internalized social forces.

The internal conflict can also develop between the protagonist and herself. However, this is not the case here, as she is struggling to overcome the supposed obstacles that others (her family) are imposing upon her. It's not that she doubts her own capabilities or competence; it's that others doubt her capabilities, based on the fact that she is a woman.