Is there a shot to stop allergies to cats? like an anti-cat allergy shot?

Yes: There is a cat extract that is available to be used on allergen immunotherapy for cat.

Allergy shots: An allergist can test you for various allergies and formulate allergy shots (immunotherapy) that will slowly build up your immune system's responce to those allergens (tolerance) over time (years). Cat allergy responds well to this therapy, when given by a properly trained allergist that follows the acaai/aaaai guidelines. See an allergist for testing and to discuss therapy options.