Will my secret sins be exposed on the Day of Judgement?

Nothing is hidden from Allah

Allah already knows every deed, public or private. The Quran says the Day of Judgement is a Day of full accountability:

That means no sin will be forgotten or missed. But being disclosed to Allah is not the same as being shamed in front of everyone. See What is the book of deeds in Islam?

The hadith of Allah's screen

Ibn Umar was asked what he had heard from the Prophet ﷺ about the private talk between Allah and a believer on that Day. He said the Prophet ﷺ taught that Allah will bring the believer near and shelter him with His screen, then ask: "Did you commit such-and-such sins?" The believer will say yes, again and again, until he thinks he is ruined. Then Allah will say, "I screened your sins in the world and I forgive them for you today," and he will be given the record of his good deeds (Sahih al-Bukhari 2441).

The same hadith contrasts this with disbelievers and hypocrites, whose lies are announced publicly. So the hope is for believers, and whether any sin is forgiven remains in Allah's hands.

Repent and do not despair

Sincere repentance erases a sin before it ever reaches the Day. Allah says:

If you struggle with a sin you keep returning to, see Will Allah forgive me if I keep committing the same sin? If you are a convert worried about your past, see Are all my sins forgiven when I become Muslim?

Keep your own sins private

Allah's concealment in this world is a mercy, and we should not throw it away. The Prophet ﷺ said that all his followers will be forgiven except those who sin openly. He gave the example of someone who commits a sin at night, though Allah has screened him, and then tells people about it in the morning (Sahih al-Bukhari 6069). Instead of boasting or confessing to others, turn to Allah privately. If you wronged a person, though, you should put that right with them as well.