Both your dreams dramatise the pit of the stomach sinking feeling.
Please try to clearly see the difference between failing an exam and the emotional pit or failure feeling that can follow. Missing a pass in the exam is simply an event, it can often be changed. The emotional reaction however, might well make you incapable of transforming failure into success.
In the second dream you nearly get swallowed up by the earth. That is precisely the situation that can happen if you cannot deal with your emotions of failure - you get swallowed up by them! Whatever you feel emotionally about yourself you live out as real if you take it as a truth instead of an emotion.
What we feel emotionally is a reaction to an event or thought, it is not a reality unless we make it so. In your case the first dream shows how this emotion has come into existence - out of feelings of living up to your parents expectations, and what they have invested in you. It would be crazy if the support you received for achievement, becomes a trip-rope to throw you down.
Tony