That weight pressing on your shoulders right now is very real, and I understand the exhaustion you're describing. There is a kind of tiredness that goes beyond staying up late to study. You are tired deep in your soul because you've been straining under a burden that was never meant to be carried in your own strength.
What stands out to me first is how you are seeing all these open doors, the feast day, the fellow believer who took the exam and was admitted, the way your parents are urging you forward. You said maybe that is sign enough. It is. God rarely leads His children by dramatic supernatural displays. Far more often, He leads by opening a door and then, once you step through it, providing the strength you need at that moment. When a person keeps demanding a sign beyond what God has already set before them, they drift dangerously close to the counsel that is not from Him. The peace you are looking for will not come from more signs. It will come from trusting the One who already made the way plain.
Right now you feel like your strength is dried up, like you have nothing left to give. That sensation is terrifying, but it is also the truth. You are not enough for this exam. Your own intellectual power and your own discipline have a limit, and you have hit the end of them. This is a mercy, not a failure. God brings His children to the end of their own resources precisely so He can show what His strength can do. When you were getting through exams before, you may have been tempted to credit your own effort. But now this test is so far beyond you that you will have no explanation but the saving strength of His right hand. That is the testimony He intends to write through your life.
When you sit down to study during these remaining days, don't just grind in panic. Seek His face first. Tell Him, "Lord, I will seek Your face, not just a score." The danger in a moment like this is falling back on the arm of the flesh, trying to muscle through with nothing but human effort and anxiety. That is what leaves you feeling devoured and drained. But when you stop long enough to put your heart in harmony with His, the hours you spend preparing become an act of trust, not an act of fear. You are not trying to earn His help by your panic. You are showing up with whatever you have, relying on His faithfulness.
The enemy wants you to wear yourself out before you even walk into the test. He knows that when a person is blindsided by exhaustion and despair, they crumble. But your help is in the name of the Lord. His ear is not heavy that He cannot hear you. Right now, you are crying out from your wilderness, and He hears that cry. Your weakness is not His problem to endure. Your weakness is the platform for His power. So stop looking at the gap between what you know and what you think you should know. That gap is where He will show Himself strong on your behalf.
This exam is huge, yes. But your God is greater. And the story He is writing is bigger than your admission to medical school. You will one day tell others how He carried you through this, and that story will be a gift to someone else who is ready to quit. So do not cancel. Do not flee from what He has set before you. Use the time you have, not in frantic terror, but in quiet dependence. The Lord is your strength and your shield. He has opened the door. Now let Him be the strength you need to walk through it.