OP I m now 49 but my anxiety at school started when I was 9 - I was always very anxious about vomiting (and pooping actually) anyway, but it ramped up when I felt ill at school and was sent home. After that, everyone and everything was a ticking time bomb, and a tummy bug or vomiting person was around every corner.
So I was very much like your daughter, and when anyone ever asked me why I was crying or had bright red rings around my eyes or refused to get on the coach or mix with anyone etc, I absolutely did not know how to articulate what my fear was because it was so intangible. I tried but didn't have the words, and in any case, when I did blurt out something simplistic like "I just want to be with my mum all the time" (i.e that's where I felt safe, away from other people), I'd get a lecture about being more grown up, so eventually I just said nothing.
When I look back, if I'd felt safe enough to be honest about what I was afraid of without getting "told off" for being needy or having histrionics as my mother called it, and if I'd been sent for CBT at a younger age (I referred myself aged 17), that would have made a huge difference.
Anxiety is much better understood these days especially in children, they didn't deal with it much in the late 70s/early 80s. CBT is amazing.
I don't know if that helps even in a small way, just trying to explain how it feels as a 10 year old! 