There is an act of contrition, and then there is perfect contrition. One is external, and the other is internal.
Let me give an example. You hit your sister, and your mother says “you apologize to your sister right now!” you of course, in that tiny voice, say “I’m sorry”. You have made an act of contrition. You may not even be truly sorry, and yet you made the act.
Perfect contrition is feeling truly sorry and in need of forgiveness. You cannot act that, it is internal and comes from the heart, or even the soul.
Perfect contrition is a sorrow for sins which is motivated from the love of God.
It contrasts with imperfect contrition, a sorrow arising from a less pure motive, such as fear of Hell.
It is the motive for sorrow rather than the intensity of feeling that distinguishes the two forms of contrition, and it is possible for perfect and imperfect contrition to be experienced simultaneously.
Unless it is properly motivated, perfect contrition rarely ever truly happens, which is why we thankfully have the sacrament of confession. If we were rely strictly on perfect contrition, our sins would seldom be forgiven. We can be contrite, we can be extremely contrite, but to be perfectly contrite is nearly impossible.
When you refer to the prayer, There is the Act of Contrition, and the Act of Perfect Contrition, but they are only acts. God sees through our acts and sees into our hearts, if our motivation does not meet what is needed for perfect contrition, there is doubt as to whether our sins are truly forgiven.
So make sure you get to confession, go with a contrite heart but along with the sorrow we have for offending our Heavenly Father, we should also rejoice in the fact that God gave us the sacrament that does indeed without doubt absolve us of our sins.