According to the Catholic Church, does purgatory have a symbol? 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.