Here is what I found in the Catholic Catechism.
"1470 In this sacrament, the sinner, placing himself before the merciful judgment of God, anticipates in a certain way the judgment to which he will be subjected at the end of his earthly life. For it is now, in this life, that we are offered the choice between life and death, and it is only by the road of conversion that we can enter the Kingdom, from which one is excluded by grave sin.79 In converting to Christ through penance and faith, the sinner passes from death to life and "does not come into judgment."80
The punishments of sin
1472 To understand this doctrine and practice of the Church, it is necessary to understand that sin has a double consequence. Grave sin deprives us of communion with God and therefore makes us incapable of eternal life, the privation of which is called the “eternal punishment” of sin. On the other hand every sin, even venial, entails an unhealthy attachment to creatures, which must be purified either here on earth, or after death in the state called Purgatory. This purification frees one from what is called the “temporal punishment” of sin. These two punishments must not be conceived of as a kind of vengeance inflicted by God from without, but as following from the very nature of sin. A conversion which proceeds from a fervent charity can attain the complete purification of the sinner in such a way that no punishment would remain.84
1473 The forgiveness of sin and restoration of communion with God entail the remission of the eternal punishment of sin, but temporal punishment of sin remains. While patiently bearing sufferings and trials of all kinds and, when the day comes, serenely facing death, the Christian must strive to accept this temporal punishment of sin as a grace. He should strive by works of mercy and charity, as well as by prayer and the various practices of penance, to put off completely the “old man” and to put on the "new man.“85”
I believe this means there is eternal punishment of sin after death, and that when we are forgiven we are free from this eternal punishment. Based on this I think that what I was taught is correct and that fear of eternal punishment is not a bad thing, as it will keep us on the right path towards salvation,