I found this in the Health Topics in direct resonse to your question!!
Allergies and genetics
Inherited allergies; Genetics and allergies
A specific allergy is not usually inherited, but the tendency to develop allergies is often passed down through families. If both parents have allergies, their child is likely to have allergies. However, your chance of develop allergies seems to be greater if your mother has allergies.
For general information on allergies and their treatment, see:
Allergy to mold, dander, dust