This may sound out there:
Ear infection.
When our vestigial thingmy (ugh. It's early here. No caffeine) gets all clogged up... Usually our balance is affected (because that's what tells our brain how we're oriented in the world: upright, tilted, moving, slowing, etc.).
HOWEVER sometimes instead / in addition to: it can affect how our brain perceives the WORLD.
A significant number of agoraphobics (fear of open spaces, often leading to "shut ins" who don't leave the house) actually have inner ear problems. Their inner ear gets messed up and as they move about they experience vertigo (which triggers fear) and nausea (which triggers revulsion). Inside their own home their brain can look at the space and acclimate by figuring out where they are by sight. But in unfamiliar areas, their brain CAN'T... So they experience fear & revulsion (from the vertigo & nausea). It's absolutely standard now that agoraphobics get a complete ENT work up.
So to ME... While its not agoraphobia... The fact that the fear is triggered while your daughter is MOVING (and especially when moving in 2 directions: fwd and up... Like when walking up stairs)... Makes me think that she may have an inner ear infection: with her brain processing that info coming from her ear wrong.
((Like I said : its before caffeine. The part of the ear I'm taking about is kind of spiral shaped. There's fluid in it. As we move, the fluid gets pushed around, and that's what tells us "where" we are in space, and "how fast" we're moving in space. While the most common thing to affect that is an inner ear infection a 'normal' ear infection, sinus infection, tooth abscess, TMJ, swollen glands, etc. can ALSO cause swelling that affects how that information is processed, or that is impinging on a nerve. These kinds of things SONETIMES have pain, but more commonly don't. So I would take her to an ENT to check out the while noggin, although most likely, it will be an ear infection... It could be something else.))
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ETA: While I do believe in spirits, and also psych stuff... I like to rule out physiological causes whenever possible FIRST. Just as an example: my son experiences panic attacks and anger outbursts. The vast majority if which are caused by a severe asymptomatic (no wheezing or coughing) asthma attack. Test his blood oxygen levels, and they're in the low 90's (90-94). 2 puffs on his inhaler, and POOF. His o2 levels jump up to 98/99, and the panic &/or tenper tantrum vanishes. Both are his body responding to not having enough oxygen. He also gets VERY goofy. Sometimes that's just him (ADHD). Other times? His o2 is in the 80's and he's actually "high" from o2 deprivation. Again. Asymptomatic asthma. Open up his airways and he's right as rain.