What is the interpretation of my feeling shivers, crying, and comfort when supplicating for marriage to a specific girl, even though all indications point to its impossibility?

It is not possible to definitively interpret what happened to you; it could be normal due to your strong desire to marry the girl and your emotional state. If the girl is engaged, it is not permissible for you to pray for her to be your wife. However, if her engagement has not been agreed upon, there is no harm in praying that Allah facilitates your marriage to her if she possesses good character and religious commitment. If it is facilitated, then praise be to Allah; otherwise, seek someone else.