You're quite right. Your parents brought you up well, or they gave you a good upbringing. Both are correct. On the other hand, school gave you a good education, unless your parents taught you at home! Education usually refers to formal learning, whereas upbringing is more informal life skills.

Your parents raise you which includes physical care, emotional care, guidance, and education. (Crecer) Your teachers focus on educating you. (enseñar) The sentences you wrote as examples were very good.