Just some suggestions . . .
1.After failing the university entrance exam, I didn't have the confidence to start studying again in order to apply to another university.
2.It seemed difficult to get accepted to xx university.
3. The cross country travel experience was my turning point. After that, I decided to apply to your school.
4. Also, I developed a stronger self-confidence after successfully finishing cross country travel.
5. After traveling, I began to prepare the application to your school