I haven't found it on the internet. Are there any symbols for purgatory, or related to purgatory?
No, there is no definite symbol for purgatory. There is nothing that when you look at it, you will think "that means purgatory".
The "fish" IXOYE is one of the many symbols of Jesus, as is the "Chi Rho" symbol: ☧, ⳩
The cross is a symbol of Christianity: ✝
But there is nothing of the sort for purgatory. But there is also no definite Christian symbol for hell, or for heaven. Sometimes, cleansing "Holy Fire" is used in art in conjunction with purgatory, but this is not exactly a symbol in the relevant sense. Keep in mind also that, to take one prominent example, it is not a doctrine of the Catholic Church that purgatory is a place: it might only be a process of cleansing. For that reason, a symbol might be even harder to come by.
There's no official symbols for purgatory, I don't think so.
But there are iconographic and traditional symbols, used in traditional literature, painting, etc...
For instance, the bridge.
Dans la religion chrétienne enfin, le pont est par association lié au Purgatoire.
Translation: In christian religion, bridge is associated with purgagory.
You can find this brige theme in Jacques de Voragine's "Golden legend" or Dante.
According to the Catholic Church, does purgatory have a symbol?
There is in fact a symbol for Purgatory.
The symbol for purgatory is the flames of a fire. Catholic religious medals and other objects have no other symbolism than this. Catholic theology does not even define the nature of suffering of the souls in purgatory and the purifying flames of mercy is the only symbolism of purgatory one will ever see in Catholic culture. Just as gold is purified by fire, so too are we when we must see the Face of God as he is.
That there is fire in purgatory is not a clear teaching of the Church – Garrigou-Lagrange considers it a sententia probabilissima (the most probable doctrine), but not a defined teaching of the Church. He notes that the Council of Florence did not condemn the Greek schismatics who denied the existence of fire in purgatory, though it does favor the common Latin opinion affirming the presence of material fire there.
On the other hand, it is important to mention that the Church has not rejected the possibility of material fire in purgatory. The Catechism of the Catholic Church (CCC 1030-1032) refers to the fire and flames of purgatory twice, never indicating that these flames are metaphorical. Thus, the Church seems to feel bound to at least allow for the possibility of a strictly literal interpretation of the purifying fire and uses the language of fire and of flames without any hint that this is meant metaphorically. - Is there fire in Purgatory?
Let us start with heaven! The symbol for heaven is a pearl.
The pearl is symbolic of the kingdom of heaven, and is taken from Jesus' parable of the "pearl of great price." Matthew's gospel also uses the pearl as a symbol of the word of God. Matt. 13:45 "Again, the kingdom of heaven is like a merchant looking for fine pearls. 46 When he found one of great value, he went away and sold everything he had and bought it. (NIV)
Matt. 7:6 "Do not give dogs what is sacred; do not throw your pearls to pigs. If you do, they may trample them under their feet, and then turn and tear you to pieces. (NIV)
In Catholic symbolism of the labyrinth is the symbol of both hell and the pilgrim's way.
This is the labyrinth at Notre Dame de Chartres (France).
The Symbol for purgatory is souls being purified in flames as is gold is in the fire. The souls in purgatory are often seen reaching their arms out to the Virgin Mary for aid in their distress. The Basilica of Our Lady of Monligeon, France is dedicated to the souls in purgatory under the title of Our Lady of Deliverance.
We can see this symbolism in in both Christian art and in pious religious medals!
Catholic religious medals tend to have the Souls in Purgatory reaching out to Jesus on the Cross thus symbolizing their need for His Mercy! In both cases the souls of the dead are in the purifying flames of purgatory.
Purgatory purifies the soul before the soul’s grand entrance into heaven.
Pope Benedict XVI recommended to theologians the presentation of purgatory by Saint Catherine of Genoa, for whom purgatory is not an external but an inner fire: "The Saint speaks of the soul's journey of purification on the way to full communion with God, starting from her own experience of profound sorrow for the sins committed, in comparison with God's infinite love. [...] 'The soul', Catherine says, 'presents itself to God still bound to the desires and suffering that derive from sin and this makes it impossible for it to enjoy the beatific vision of God'. Catherine asserts that God is so pure and holy that a soul stained by sin cannot be in the presence of the divine majesty. We too feel how distant we are, how full we are of so many things that we cannot see God. The soul is aware of the immense love and perfect justice of God and consequently suffers for having failed to respond in a correct and perfect way to this love; and love for God itself becomes a flame, love itself cleanses it from the residue of sin." - Purgatory (Wikipedia)
The Church has never defined how the Poor Souls in purgatory are actually purified, thus fire and /or flames remain a valid symbol for Purgatory.