Can a trapped nerve cause vertgo?

Yes: There is a "balance nerve" also called 8th cranial nerve that connect your inner ear (with your balance organ) to the brain. Compression of this nerve causes among other things dizziness.

Several causes: Vertigo is a symptom of tumors afflicting the eighth nerve, external or internal compression, but also may get inflamed, swollen, and cause an imbalance of brain sensations (vertigo!). A rare post-traumatic condition termed barre-leiou syndrome can cause vertigo due to nerve compression in the neck affecting autonomic nerves.