Why would she have issues over hearing singing? That's not why they died. If she had some other gift or dream that had them travelling together for her at the time to that place, they would still be alive. Isn't this similar to survivor's remorse where the survivor feels guilty/bad about still having access to their wealth/dreams/good life ?
No, it is because she wanted to go to a music concert, she blames herself for wanting to go, feeling like its her fault, she stops singing because of her selfish desires that "caused" her parents death, most likely not wanting anyone else to suffer or fall under a similar fate due to her misfortune.
I can interpret it as that.
If your parent's die in a car crash while going somewhere, but because you wanted to go there, you had them take you, you would probably blame yourself if it was an accident, you would think it was avoidable if you didn't tell them to take you, if you just hadnt asked.
You would be blaming yourself because it was seen as avoidable.
So, let me get this right. Lucia and her parents were going to see a singer, and they got hit by a cart... So instead of having PTSD of carts or horses, she's scared to sing, NOT OF HEARING SINGING, OF SINGING HERSELF.