She is a pleasant 18-year-old female who states that she was at a pub where she was eating and actually fell while holding a tray and rolled her ankle.

A) complete sentence
B) fragment
C) run-on

My first thought is C) run-on, but I always second guess myself. Now I think it might actually be a complete sentence, since it could work without commas?

Yes, it's a complete sentence -- even though convoluted.

The subject and verbs of the main clause is "She is, fell, rolled."