Question: My mother is allergic to bee stings. Does that mean I am allergic as well?
Answer: Probably not. It is true that if your parents are allergic, there's a great risk that you will also have some form of allergic disease. But it's generally not true that you'll be allergic to the same things as your parents.
Remember that allergy occurs when there's the right genetic combination -- the genes you get from your parents -- but also certain exposure to something in the environment -- in this case a bee sting. So it's possible that if were stung by a bee you may develop allergy based on your genetic background. But this generally isn't the case. Unfortunately the only way to know for sure is for the person to be stung -- which is something you hope to avoid. In any case I wouldn't have a great deal of concern about having this specific allergy, but you should be aware that it's possible you'll get some allergic condition during your lifetime.