The common teaching of the Church is that the pains of Hell are due to actual sins committed, whereas the punishment of original sin is the deprivation of the beatific vision. Theologians have had two main opinions on the experience those who die in original sin only, but have not committed any actual sins (basically unbaptized infants and unbaptized persons incapable of sin). They all must agree that they are deprived of the beatific vision (this is dogma), but some argue that the deprivation of the beatific vision is painful and tormenting, and others that it is merely a state of natural happiness (rather than supernatural happiness). This latter state is what is called Limbo.
So, as Catholics, we are permitted to hold either opinion regarding those who die in original sin. We cannot say that those who die in original sin are saved.
That being said, while we acknowledge that God has only revealed one way to remit original sin–baptism–we also acknowledge that God can remit it in ways known only to himself. Therefore, it is permissable to hope that God might in an extraordinary way cleanse an infant of original sin who has otherwise died without baptism. Such a soul would therefore not die in original sin, but with sanctifying grace and would therefore go to Heaven. In the Summa, St. Thomas says God could do this as a kind of privilege if he chose, but He has not revealed it one way or the other.