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...

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.