Not necessarily. It depends on what the allergen is and what the reaction is. There's no reason to worry about a reaction that hasn't happened yet.
Not allergies are like peanut allergy. A severe reaction doesn't have to be throat closing or hives.
For instance, I am sensitive (allergic my allergist calls it) to sulfites. My reaction to that can start in a half hour to 2 hours. I don't get swelling in the throat, but I do get tachycardia, which once triggered a heart attack and has sent me to the hospital a few times.
Or, my allergy/sensitivity to albuterol - which started 8 hours after I inhaled a puff and put me in the hospital.
A severe allergy can happen the first time you come in contact with the allergen, or the second, or even after years.
Do you have a particular reaction? Do you think you may be allergic to something?