I think you have to figure out if it's actual car sickness vs anxiety.
One of my kids gets anxiety (every few years) and it manifests as stomach upset. She will belch and gets a mouthful of vomit (that's the extent of it). Mostly though, just nausea and it passes.
She learned relaxation techniques. These helped tremendously. I've listed them now a number of times - you can Google them. Essentially they involve breathing. Anxiety with kids kind of involves their feelings/bodies speeding up, so I think of it as slowing them down .... and a good one for my kid is to get them distracted - focus on 5 things you can hear, touch, smell, etc. with the breathing.
Another exercise is - what's the worst that can happen? What's likely to happen? (and you come up with plans). When it's done, you say "What happened?" it's likely a good experience. You keep reiterating that the worst cases never happened. It's empowering.
You work on empowering your kid. Get her into activities where she feels stronger as a kid, where she takes risks and does well. Could be climbing a tree, doing a cartwheel, riding bike, calling a friend, ... whatever it is.
Breathing though is where you typically start.
For your daughter if it's getting out of house, baby steps. Start small - short little trips, to local ice cream store, or whatever. I would come up with things she'd like to do.
I don't really know much about agoraphobia - I think maybe some sessions with a child psychologist would be helpful.
Does she open up? They have a hard time talking about it - because anxiety feels physical - she may just feel car sick. A therapist can get her to explain it or you can look online - lots of resources. Good luck :)