Antibiotics prevent. Antibiotics are given to help prevent transmitting a possible infection to the baby. The risks and benefits of all drugs given to a women who is pregnant need to be determined and discussed with her.
No. A child's immune system doesn't really "wake up" until several months after birth, so exposure to allergens in utero will not lead to specific allergies in the child.
No. If anything, fetuses are more likely to tolerate substances that their mother received during pregnancy - not become allergic to them. Antibiotics in labor are a major progress in decreasing perinatal mortality and are vastly safer than risky for any given mother-infant pair. Having said that, allergic reactions are inherently unpredictable and poorly understood.