I have never heard of sensitive child syndrome.
I agree with the other suggestions. Arm her with the ability to answer her own questions. She's still allowed to verbalise them, that's fine, she's still only very little. But give her the courage and confidence to see her own answers and know that having her own thoughts about it are ok and not right or wrong.

I am the parent of a child with anxiety. He is unable to watch ABC kids tv because he struggles with the issues that arise, and no matter how many times he sees Thomas the Tank engine end happily, he still cannot cope with the storyline. And he's nearly 6. So, some children just are more sensitive in some ways.

I can't see why anyone would think your darling daughter is awful. That's not a nice thing for someone to say to you. She might just be a child who needs to be helped with her emotions more than most children. But at least she is not holding the emotion in and she trusts you to share it with you and wants you to help and support her. Keep that up, then you don't have to worry about her internalising it all, and perhaps dwelling on it alone and in silence.

I needed the help of a child psychologist as I was struggling to support my DS with his anxiety. There is no harm in asking for help. I am much happier and calmer with him now and I am less concerned about his behaviour, and my reactions to him are more consistent and calmer now too.