Birth control pills can have allergic reaction. But, the allergy is person specific and not general. The major reason behind the allergy is the ingredient of birth control pills. They contain a milk protein called lactose. Many people have allergy towards lactose and if you do not like milk products the pills might create some allergy.

The second reason behind birth control pills causing allergy is that they are capable of creating hormonal disorder in your body. They affect adrenalin and secretion from thyroid glands.  Thyroid imbalance is the major cause of allergic reaction in many women after consuming birth control pills. Adrenalin imbalance might lead towards allergy when there is a sudden impulsive reaction. Yeast and allergy are related with each other. Birth control pills stimulate the growth of yeast. 

The growth generally occurs at the vaginal tract and location. These yeasts are also capable of weakening immune system of our body. Excessive growth of yeast in many cases is the reason behind allergic reaction.  Proper medical checkup is pivotal to reduce the allergic reaction caused by birth control pills. You are advised to consult doctor before consuming these pills to avoid any allergy.