I am writing an essay on a story called "The Love of My Life." I am having trouble finding the complications.
(This stroy is about two teenagers who had a baby in a motel and threw the baby in a dumpster and left to die.)
It sounds like you are writing about Boyle's short story published in the New Yorker.
Short stories typically follow a very basic storyline which starts with a conflict (or the main problem), builds through rising action toward the climax (highest point of action), and ends with a resolution (the solution to the original conflict. Complications in a storyline are the details which arise as the characters move toward a solution (or the resolution) for their original problem. Complications are the plot twists and turns which keep stories interesting.
In order to determine the complications of this story, you must start with the most important conflict. China and Jeremy are high school sweethearts. On the day they are leaving to go to separate colleges, China tells Jeremy she is pregnant. Conflict: what is China going to do, both through the pregnancy and after, with a baby?
The first complication is actually presented before the conflict. The parents of this baby are young and they are not going to be together during the pregnancy (separate colleges). Other complications include their desire to hide the pregnancy rather than seek help, her refusal to get an abortion, and the strain on their now distant relationship which results in several arguments and fights.
Ironically, the complications in this story are what lead the couple to the tragic climax. As you know from reading, the resolution to the original conflict is not a happy one. Like many stories (take "Romeo and Juliet" for example) involving youth, love, and mature circumstances, poor decisions become the bulk of the complications which only lead to further poor decisions and ultimately, a tragic ending.