I'm not in any way qualified to give advice on children, so know that ahead of time. Not a psychologist and not a mum. But what if you were to create a conversation with her about how it's okay to feel yucky about things sometimes. That proves that she's a very caring individual and you admire that about her. So, validate her feeling.
And then say you'd like to help her feel better, but you need some help. What does she think might help when she feels yucky? You could come up with a mantra with her she might repeat, "All of my family members love me very much" (I'm unsure on this one - perhaps too emotional for her) or, "I am going to be okay" or "Today I will do something nice for someone". Or, maybe she responds well to deep breathing and you can practice together. Or maybe she can carry a small craft around with her and when she gets nervous she can give herself a little break to work on the craft or read a book. You sound like a great dad who does this kind of thing.
