I have been in this situation as my dd has chronic pain problems, which understandably made her reluctant to go to school or at times to face life at all. At the same time, she also said she did not really want home education and she was clearly thriving on the academic and social side of school- she just panicked when it was time to go and she started worrying about not coping with a whole day at school. I know all about dragging a screaming hysterical child out of the house and walking away from the school crying with exhaustion after she'd gone in. The accusations of "not believing me" were particularly painful to me, as the first doctor who saw her did in fact believe she was making it up and told us so- so some of that has stuck. Still, I believe I did right: some kids with her condition have ended up complete invalids, with no friends and little education; she too recognises that she has done better than them.
But I know how hard it is.
A couple of points strike me:
Home education may be fine if it is a positive choice you have made because you feel it is beneficial.
What is not beneficial is letting her give in to a momentary panic, this is not setting her up with the life skills she needs. If she stays at home, it must be because you judge that she is not fit to go. Never let her see that you are not strong enough to manage her, that will frighten her more than anything.
Get help if you need to. If it hasn't cleared up by next term, ask your GP for a referral. School phobia can be treated.
If this becomes a habit, the school will send the truancy officer around. Education is compulsory, to keep her at home you need to register her as home educated. If not, somebody from social or educational services will almost certainly come to see you- it probably looks good if you contact them first.
Recognise her fears and talk to her about them when she calms down. Let her know that many people feel like this when they've been ill. Explain to her that it is possible to learn to control these fears. Maybe teach some relaxation techniques.
Also explain to her what the law says, so she knows it isn't just you being mean.