I sometimes think that if I just do more and more good works, my past mistakes will be buried and I’ll be safe. Is that how it works?

Yes, in part, and it is worth knowing exactly how. Good deeds really do have the power to wash away what came before, and Allah has promised this plainly:

“Indeed, good deeds do away with misdeeds.”

Qur’an, Hud 11:114 · meaning

This promise speaks first of the slips and stumbles that dust a believer’s feet along the road. Where something heavier weighs on you, the door of turning back to Him is open as well. A word of sorrow spoken to Him alone, a firm intention not to walk that way again, and where another person’s right or heart was touched, a quiet setting of it right: with these the heavier things are lifted too, so that nothing at all need remain between you and Him. That is how the people of knowledge have always read the verse. Notice that there is no scolding in it anywhere. There are two doors, both of them open, both of them His mercy.

So your instinct is sound. The Prophet, peace be upon him, gave the same medicine in the simplest words, so that no heart would ever despair:

“And follow up a bad deed with a good deed and it will wipe it out.”

The Prophet (peace be upon him), Jami’ at-Tirmidhi (1987) · meaning

But set one thought beside your hope. Good deeds are not bricks you pile over a buried thing to keep it out of sight. They are clear water you keep pouring, so that the heart stays washed and bright. The difference lies in the posture within. When deeds are heaped up only to feel safe, the eye keeps drifting back to the tally. When you do good because you love Allah and love to please Him, and you turn back to Him for whatever needs turning back, the past dissolves on its own, and something better than safety grows in its place: nearness.

So do the good deed, then do the next one, and let each be an act of love rather than a payment. Your mistakes are not a wall you have to climb. The small ones that gather on a traveller’s feet are more like footprints on wet sand, and the next tide of goodness smooths them away. For anything that lies deeper, one sincere turning of the face toward Him is enough, because He draws near to a returning heart before that heart has finished its first step.

And when a moment of forgetfulness does slip through, as it does for every traveller, do not sit down in sorrow over it. Reach for the very next small thing: a kindness, a prayer, a quiet remembrance, and let that be the good deed that follows and wipes clean. This is not anxious accounting. It is a rhythm of return that keeps the heart soft and hopeful.

One small step: The next time a small slip troubles you, do not dwell on it. Offer one tiny good act right away, a single sincere “astaghfirullah,” a smile, a coin given quietly, and let that be your good deed following the lesser one.