Hello. I'm sorry you're having to deal with this situation. For what it's worth,
disability determination isn't the sole purview of a physician. Your doctor's evaluation is certainly a part of the process, but disability is usually only granted if a person's medical disorder prevents him or her from participating in ANY gainful employment (not just your usual occupation), and they also must have been unable to work for a year or more due to their disabling condition.
Furthermore, if there are any treatments that have not been tried in an effort to deal with your
cold urticaria (e.g., daily antihistamines, H2 blockers,
corticosteroids, etc.), an independent medical examiner might recommend a trial of more intensive medical therapy before disability is considered.
In short, you should talk with your doctor about initiating the disability process. If he/she feels your urticaria is a disabling disorder, you can take it from there.
I hope things go well for you!