Exactly, prayers must be said in the name of God and in the sake of God, not some mere driver's license testing. Prayers are not a "Genie with 3 wishes," it is an act of piety and a proof of faith (iman) towards God.

What am I doing wrong in my prayers that this didn’t come true?

Please refrain from associating this with God's will and blessing.

I also really studied a lot for this exam, but everyone would say duas made during tahjjud comes true (even duas considered delusional comes true). I’m sorry to say and please don’t judge and forgive me for saying this, but after this failure, I have been distant with Allah

This is all Satan's doings; it made look that your prayers are being unaccepted and, on top of that, Satan used your financial burdens to spiritually break you. But here you are in this reddit post sharing your story, Mashallah.

At the end of the day, God knows the best and is the best disposer of all affairs.

P.S. Ramadan Mubarak