Can someone have an allergic reaction to shrimp cooking?

Yes: any one can have food allergies. in fact sea food allergies are the one of the commonest food allergies.

Yes: Even inhaling fumes containing allergen can cause allergic reaction.

Unlikely: but if extremely allergic to shellfish/shrimps, a person can even have a problem smelling or touching the material, although rare. As a precaution should avoid tasting it or the soup, and keep emergency medicine, epinephrine and antihistamine, handy, best wishes