The first major conflict in The Face on the Milk Carton by Caroline B. Cooney is the one that occurs when Janie sees the picture on the milk carton and recognizes that the kidnapped girl in the picture is actually herself at the age of three, wearing a dress she can remember. This causes an internal conflict about her identity.
Her next conflict is with her adopted parents Frank and Miranda. She wants to find out more about her birth parents and the circumstances of her kidnapping but they want to protect her and themselves from possible legal complications and also from the cult.
Her final set of major conflicts has to do with her love interest, Reeve. There are parental obstacles to their relationship, his desire to go further with her sexually than she is comfortable with, and their temporary breakup due to his discomfort with her not telling the truth to her family.