There is pain and suffereing in purgatory. But it is a purifying punishment. Not punishment for the sake of punishment. It prepares us for God.
You are doing very well, Papist, but it will take one or two more steps before you grasp the full concept of purgatory and its purpose.
Let's look at the Council of Trent - and its infallible teaching. The Pope and bishops teach that the purpose of purgatory is the expiation of sin, or the discharge of the debt of temporal punishment
"If anyone says that after the reception of the grace of justification
the guilt is so remitted and the debt of eternal punishment so blotted
out to every repentant sinner, that no debt of temporal punishment
remains to be discharged either in this world or in purgatory before
the gates of heaven can be opened, let him be anathema."
~ Trent, Canon 30.
Also the Catechism of the Catholic Church speaks about "those who are expiating their sins in purgatory."
CCC 1475: "In the communion of saints, "a perennial link of charity
exists between the faithful who have already reached their heavenly home,
those who are expiating their sins in purgatory and those who are still
pilgrims on earth. between them there is, too, an abundant exchange of all
good things." In this wonderful exchange, the holiness of one profits others,
well beyond the harm that the sin of one could cause others. Thus recourse
to the communion of saints lets the contrite sinner be more promptly and
efficaciously purified of the punishments for sin."
Notice the vocabulary - guilt, debt, temporal punishment, expiation, punishments for sin.