Rome strongly condemned Pelagius at both Carthage and at the II Synod of Orange in 529 A.D., so it would be foolish of me to charge the church with Pelagianism. In my view, if pressed, I would say that when it comes to the doctrines of grace as the Reformers expounded it, Rome more closely resembles something like an Arminian position. If there is another theological category that is more accurate, I would certainly be willing to consider it.
...the Catholic Church does not teach that we can get to heaven through our works or as a result of personal merit. It is God's grace that saves.
We are in agreement regarding grace, as far as that goes, but it is a rather broad statement. We must then ask the following:
Is it a grace that saves, that is, actually accomplishes salvation, or merely makes it possible for us to attain it?
Did Christ die for all men, that is, did His death atone for the sins of all mankind, or only for believers, those whom the Father has given to Him (John 6)?
If the atonement pays for the sins of all men for all time, why should there be any men in hell?
Why must we make "satisfaction" for sins committed in this life if Christ has paid for them at the cross?
The Reformers expounded that it is Christ's righteousness which merits the sinner's forensic declaration "just" in God's eyes (simul justus et peccator = at the same time just and sinner), which Rome regards as a "legal fiction," a slander against the holy nature and character of God. Rather, the Catholic church proclaims a righteousness which, though not inherently beginning within the sinner, nevertheless becomes his own through the infusion of Christ's righteousness into him; a making just. This grace, in Rome's view, is then something with which the sinner cooperates (assentire et cooperare) in his justification.
If you are saying that a personal merit that is of yourself will not by itself merit salvation (broadly speaking), then we are also in agreement there. This being our understanding, it's clear that Rome nevertheless sees merit in the works of the individual as grace is poured into him, otherwise we would have no cause to speak of the necessity of a "treasury of merit," purgatory, the special holiness of Saints, etc. So grace, as you have said, is something given by God which, through faith, begins the process of justification. I think it's overly simplistic and unfair to accuse Catholics of advocating a salvation by works which is no different than what is understood by all the other man-centred pagan religions.
The Reformers looked at salvation as the overarching theme with justification, sanctification and glorification as the subsets of it. Justification is an event, the declaration "just" of God upon the sinner (monergism), sanctification is a process,the growing in grace the whole life long, becoming more and more obedient by cooperating with His grace (synergism), and then finally eternal glorification at His coming. I agree with all those who say that we cannot work our way to heaven. Both communions would say that our works have a place in our salvation. But the Reformers said that our works have no place in our justification, as they relate to the fruits of belief and faith.