Contrition is a matter of the will, not of emotion. Your emotions can reflect your will and they can help you feel catharsis, but (and I’m speaking as somebody who is a big crier in the confessional), they aren’t as important as your realization that you did wrong. If you secretly don’t think you did anything wrong, or that it wasn’t a big deal to sin, that’s a lot more reason to worry than not having some appropriate amount of sad feelings. You can’t control your emotions, but you can form your own will.
First off, you should know that anywhere in the Bible where it speaks of having a contrite “heart,” it could also be translated as “mind.” Jews believed that the heart was the seat of thought as well as of feelings, so that’s reflected in the Bible’s imagery. Latin also didn’t feel there was much difference between “mens,” mind, and “cor,” heart. (Nowadays, we think that the brain is the seat of thought and emotion, and yet our poetry doesn’t reflect that yet!)
Second, you should remember the parable about which brother did his father’s will - the one who agreed to go work and didn’t, or the one who blew off his dad’s request but then went and did the work? Being contrite is being the second brother. Jesus doesn’t care as much about appropriate talk and appropriate feelings as he does about appropriate acts! Making reparation and doing the right thing shows you are contrite, much louder than words or feelings.
Third, if it bothers you or if you think it would be helpful, it is totally okay to use spiritual reading to make yourself feel (or think) sorrier for your sin. Acts of Contrition are often designed to help yourself understand the seriousness of sin at gut level. (Heh, there’s another piece of organ imagery!) Meditating on the Passion is very good for helping you have more contrition, which is one reason the Sorrowful Mysteries of the Rosary are so popular of a spiritual practice. But there’s also the Stations of the Cross and a ton of other ways to go, including just reading the Passion parts of the Gospels.
Never beat yourself up about your emotions being appropriate or not. Feel free to talk to a priest or somebody who can help you with spiritual direction, if you want to know if you’re doing the right things with your spiritual life.