Is having big labia minora normal for a teenage girl ?

Yes: It is just the way she developed.

Possibly.: Really depends on the physical examination; “big” may mean different things to different people. It is normal to have labia minora tissue “prolapse” pass the labia majora tissue. However, if the “big” labia minora tissue is symptomatic ( wearing certain clothing and/or during exercise, riding bikes/horses etc.) labia minora reduction surgery may be indicated.

Eye of beholder: In the context of being big, most individuals refer to the inner labia protruding past the outer labia. Teenage girls who are thin may experience disproportionately small labia majora (outer) lips which may make the inner labia appear more prominent and therefore bigger. While labia reduction can be performed, true labia hypertrophy, typically larger than 4 cm should be evaluated by qualified md.

Probably.: The size of the labia varies quite a bit and is in most cases considered "normal." even women with "normal" sized labiae may have issues with them however.