Yes, it is possible to get an H-1B for UX design, but it depends on how your job is classified. UX design can fall under multiple fields, such as computer science, graphic design, ergonomic engineering, human factors design, or industrial psychology.
To qualify for an H-1B, your role must clearly require a specialized degree in a related field. Work with your lawyer to determine the best classification based on your job duties and educational background. Careful planning is essential to ensure a strong case.