Does having an antibiotic drip while in labor cause antibiotic allergies in the baby being born?

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. There are several reasons why your doctor might recommend antibiotics in labor. This is common for gbs (group b strep) infections and if there is a concern for other infections during labor. The recommended antibiotics are safe and are not associated with allergies to medications later in life.
Unlikely. There is no data which suggests that maternal antibiotics administered during labor predispose an infant to antibiotic allergy.
No. The antibiotics given are to prevent a horrible newborn infection called group b strep. This exposure is not associated with allergies as the children grow up.
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.