My teeth are crowded, is that because of high arch?

Discrepancy. Your teeth are crowded because you have too much tooth material for amount of supporting bone material. If upper jaw too narrow compared to lower, expanding upper jaw may provide additional supporting bone. See a qualified Orthodontic Specialist for evaluation.
Might be. A high arch is caused by the overeruption of upper teeth usually due to mouth breathing. The top of the palate is where it should be, but as the teeth erupt they bring the alveolar bone down with them increasing the height of the upper teeth downwards. The treatment is intruding the upper teeth either with orthodontics or surgery.