Does the Catholic Church believe that we become just souls after we die?
The short answer is yes!
But the Catholic Church also teaches that when we die, our souls are separated from our earthly bodies. However our earthly bodies will be reunited with our souls at the general judgement.
This is why the Church technically refers to souls in Heaven as saints and not as persons. For the human person is technically composed as having a soul united with an earthly body! This will all change at the end of times!
Nevertheless, many refer to the saints in Heaven as saints. The souls in purgatory are interestingly enough referred to as the Souls in Purgatory!
Our Church teaches that immediately after death, our soul separates from our earthly body and we stand before God for judgement. We then enter heaven, Purgatory or hell.
Heaven is the ultimate end and fulfillment of the deepest human longings, the state of supreme, definitive happiness. Those who are free from all sin enter heaven immediately.
Purgatory is a place of purification, for those who die in a state of grace and friendship with God but who are not yet fully purified. Those in Purgatory are assured a place in heaven after their purification. We pray for those in Purgatory, that they may soon be with God in heaven.
Hell is for those who have willingly chosen to reject God and his love. If we persist in a state of serious sin, we damn ourselves to hell.
At the end of time, our Lord will come again to judge the living and the dead. All souls will be rejoined with their bodies, and those in Purgatory will be joined to the blessed in heaven. The Last Judgement will reveal that God’s justice triumphs over all the injustices committed by his creatures and that God’s love is stronger than death. What Happens to Us After We Die?
The following article on The Human Person is quite informative:
The unity of soul and body
Man is not merely a body (that is materialism). Nor is he merely a soul (that is spiritualism). Nor is he two beings, like a ghost in a machine (that is dualism). He is one being in two dimensions, bodily and spiritual. “The unity of soul and body is so profound that one has to consider the soul to be the ‘form’ of the body [‘form’ here meaning not ‘external shape’ but ‘intrinsic meaning’]:234 i.e., it is because of its spiritual soul that the body made of matter becomes a living human body; spirit and matter, in man, are not two natures united, but rather their union forms a single nature” (CCC 365).
The human soul is not imprisoned in the body, as Plato taught, but expressed in it, as the meaning of a play is expressed in its words. And the body is not enslaved by the soul but fulfilled by it, as a beautiful piece of marble is fulfilled and brought to perfection in a great work of sculpture.
The human soul
The human soul is not a pure spirit, like an angel. It is the “form” of the body; it is meant to inform a body. The body is not a house and the soul is not a ghost. We are not haunted! The soul is not something strange, occult, or alien. Just the opposite. It is who we are; it is our personality. God gave it to us at conception (that magical moment that was also the beginning of our body), and we shape it through all of life’s choices.
The Church’s most important teachings about the soul are “1 that every spiritual soul is created immediately by God – it is not ‘produced’ by the parents – 2 and also that it is immortal: it does not perish when it separates from the body at death, and  it will be reunited with the body at the final Resurrection 235” (CCC 366).
On each of these three points there is good reason for our faith:
The soul must be created rather than evolved, because matter cannot make spirit any more than space can make time or color can make sound. They are two different dimensions. “You can’t get blood from a stone,” and you can’t get self-consciousness and free will from atoms and molecules.
The soul must be immortal because it is not made of atoms spread out in space and capable of being cut into parts. It is not composed, so it cannot be decomposed.
The soul must be reunited with a new body because God made man as a soul-body unity, and God makes no mistakes. Therefore the resurrection of the body is needed to complete and perfect our human nature in Heaven. (Between death and resurrection, we are incomplete.) We do not become angels any more than we become ants.