Cat has diarrhea.

Hi, Our cat has diarrhea - it seems that she licks and licks herself and then it happens (the diarrhea) or it just happens .... Her anus is also red and swollen . Now we have taken her to the vet, he gave her a couple of injections and she was okay for the afternoon. Now unfortunately we were told to keep her in for a couple of days but our 3 year old daughter let her out :( The vet mentioned to us that he thinks that she has been mated with and that also could be why bottom is so red. Now unfortunately again after she came back after being out, the diarrhea has started up again poor thing. Now we inherited our cat (we were only meant to look after her for a couple of weeks) but now she is ours and a much loved part of our family. But we were told that she had been sprayed or fixed sorry not sure of the corrected terminology is there anyway just by looking at her I can tell for sure. Also we live in Greece and vet language is not really in my vocab so if I can go with some extra knowledge and advice when I take her back to the vet (in english and get someone here to help me translate my questions) that would be really helpful. Please any help will be great. I just hate thinking that she is in pain or sick in anyway.
Ps she doesn't have worms.

Sorry as we are also paying for a vet I just cannot afford to pay more please don't take this as we don't love our cat we truly do she thinks she is a second daughter and as treated like one