I'm worried because my boyfriend is allergic to the cat..move on or find my precious gizmo another home, what do you suggest?

I think this will : Take some soul searching on your part. What are your priorities? What do you value? Is the relationship with your boyfriend one that you believe might be lasting ; contribute to your happiness and well being or it is more casual dating. You have already mentioned that gizmo is precious to you. I can't recommend what action you take -but ask yourself what gives your life meaning. Take care.