Repentance precedes forgivness

"For you take no delight in sacrifice; were I to give a burnt offering, you would not be pleased.
The sacrifice acceptable to God is a broken spirit; a broken and contrite heart, O God, you will not despise."
(Psalms 51:16-17)

The word frequently translated as "repentance" in the New Testament is the Greek word "metanoia", this word means more than the English word "repent". Metanoia means to sustain a complete change of mind and heart, it's more than mere sorrow, it's a conversion of the heart. The import of that word fits very well with how God told His people to turn back to Him when they'd drifted away:
"if my people who are called by my name humble themselves, and pray and seek my face, and turn from their wicked ways, then I will hear from heaven, and will forgive their sin and heal their land." (2 Chronicles 2:14)
These words, that God spoke to Solomon are still valid for us today. We must experience a conversion of heart to God and let Him heal us through the sacrament that He gave us.

Was your confession valid? Were you really absolved of all your sins? Are you truly forgiven?
These are all questions we may ask ourselves, especially after confessing a mortal sin(s) that was really weighing on our conscience. The answer to the question is; it depends.

Now don't get me wrong, if you confess all the mortal sins you are aware of, are truly sorry, make a firm purpose of amendment to try and avoid sin in the future, and receive absolution from the priest, then you are forgiven. But that whole process really hinges on one central element; contrition.
When the priest instructs you to make an act of contrition, he isn't telling you to just say some words you memorized in school or even some confessionals have it printed on the wall. He is asking you to tell God that you are sorry. Being actually sorry, and just saying the words are two completely different things!

Let's talk about contrition for a moment. The Church recognizes two kinds of contrition;
1. Imperfect contrition:
This is when you are sorry for your sins, but only because you know that God is just, and what you have done was of grave matter and has consequently severed your relationship with Him. Therefore, you are sorry because you fear the potential punishment of hell. This degree of contrition is enough to be forgiven in the sacrament of reconciliation, if you make a full confession and receive absolution.
2. Perfect contrition
This kind of sorrow for your sin means you are sorry for your sins, not just out of fear of punishment, but because you know you have damaged your relationship with a kind and loving God. This degree of contrition stems from your love of God and is sufficient for the forgiveness of the sin, even before you go to Confession (as long as you firmly resolve to go to Confession as soon as possible CCC 1452)

So back to the confessional; if you confess, have at least imperfect contrition, and receive absolution, then you've satisfied the form and matter of the sacrament and it is valid. But here is the big problem, too many people try to make Confession into a loophole so they can live how they want, just go to Confession, and then right back to sin without skipping a beat. I have news for them though, God cannot be mocked. "Do not be deceived; God is not mocked, for whatever a man sows, that he will also reap." (Galatians 6:7)

CCC 1451:
"Among the penitent's acts contrition occupies first place. Contrition is sorrow of the soul and detestation for the sin committed, together with the resolution not to sin again"
We can see here that the sacrament of reconciliation is not efficacious (that is, it bears no effect) if the requisite repentance is not present.

Let me give you an example here:
A mafia hitman kills someone that his boss had marked for death, but since he was going to his nephew's first communion the next day, he goes to Confession. In the confessional he says he killed someone and says an act of contrition, but in his mind, he knows that latter that night he has another murder that he's been paid to carry out. Were he to mention this fact to the priest, the priest would have no choice but to deny him absolution. Part of the act of contrition is sorrow, but also a firm purpose of amendment to avoid sin. Not that we can never commit that sin again or else our absolution will be retroactively voided, but we must at least make a wholehearted effort to avoid it, and carrying out another contract killing would definitely not be avoiding it. The hitman could also choose to lie to the priest and promise to never kill again, but really having no intention of keeping that promise, I which case the absolution that he were to receive wouldn't be valid.

But what if you have a particular sin, or sins, that seem to keep repeating in your life? Something that you struggle with daily, and fail at on an almost regular basis? You can confess these sins every time you fail, and as long as you are trying not to do them, then you are making a valid confession. The point I'm trying to make isn't that we must be perfect and never commit the same sin twice, it's that we have to put in at least an effort to resist the devil. If you are having a hard time with a sin, or a habit, but you desire to be close to God and forgiven of the sin, then please go to the Sacrament of Reconciliation, and ask God for the strength to resist the devil. (A particularly powerful help in times of struggling with a habitual sin is the prayer to St Michael.) Read psalms 51 and see how torn David's heart was for offending such a loving, just and yet merciful God; pray that we will all have a heart like David whenever we fall.

None of this is to say you should worry about the state of your soul and whether or not you are in a state of grace. You should never doubt God's mercy, as Jesus told Saint Faustina "my mercy is greater than your sins and those of the whole world." What a wonderful redeemer we have, just like the Easter proclamation says "O Happy Fault that merited such and so great a Redeemer!”

St. Paul tells us to "work out our salvation with fear and trembling" (Philippians 2:12) this doesn't mean being scared of God, it means to treat your salvation as a very serious matter with all the time and attention it deserves, not as some trivial matter than can be shrugged off just because you went through the motions. Ours is a faith that is almost 2000 years old, that's 2000 years of God forgiving the sins of his people, as long as those people sincerely seek his forgiveness.

"Tear at your hearts and not your garments" is what God told Joel to say to Israel, stop the outward motions and have a conversion of the heart.

"Yet even now," says the LORD,"return to me with all your heart, with fasting, with weeping, and with mourning;
And tear your hearts and not your garments."Return to the LORD, your God, for he is gracious and merciful, slow to anger, and abounding in mercy, and repents of evil."
(Joel 2:12-13)