Not necessarily. The phenomena of having allergies could be passed down...but a lot of allergies are based on the individual person, their overall health, and health of the immune system. I've grown up with lots of airborne allergies & food allergies. I've gone to the doctor, received the shot cocktails for about 12 years, and now take Rx drugs for my allergies. None of my family members have allergies...just me.
I don't think there's a way to predict or really control allergies before the baby is born...especially the airborne particulates...unless you choose to live in a plastic bubble. If you are allergic to certain foods, you would not be eating them anyway, so that's not an issue. Breastfeeding is supposed to help with boosting the immune system and preventing allergies early in baby's life.