Hi Sara,
This is a very good question and again the differences among them are very small.
However, there are indeed some minor differences in terms of what emphasis you are trying to express.
We generally use "frightened" when you want to say that you are experiencing fear directly from someone or from someone's actions. That's why we normally say something like "I am frightened by +someone/someone's actions". "Scared" would normally describe a state in which you feel fear from a situation if it is not followed by something/someone. But if you want to say you feel fear from someone, you may also say "I am scared of+someone". The usage of "afraid" is very similar to "scared", with a slight emphasis that the fear comes from the moment you are in while "scared" is like the fear you generally feel.
I hope this helps you and should there be any other questions you are always welcome to ask! You may also check out the courses that I offer on my teacher profile if you like!
Teacher Daniel