I am just getting over a 3 month bout with hives all over. As far as we can tell (me and the dermatologist) it was caused by heat, stress and maybe an allergic reaction to something but we don't know what.
Oatmeal baths helped, and reducing contact with irritants like laundry detergent (we wash my clothes with liquid dishsoap and Oxiclean and do a triple rinse normally, so we stopped using Oxiclean and kept up the triple rinse). If you use a bath oil and it has any perfume, stop using it and try something like canola oil. If you use an acid based lotion like LacHydrin, stop using it 'til the hives are gone.
Keeping your daughter in a cool environment is an excellent idea. My hives improved incredibly when we installed an air conditioner at home.
The dermatologist prescribed some steroid creme that I used twice a day on the affected areas, and I used Benadryl when the pain or itching was too much for me to cope with.
Wearing anything, even if it was loose would make the area it covered very irritated. When she does need to wear something try to make it something as lightweight and loose as possible, with a minimum amount of seams. Seams in clothing hurt very very badly.
You didn't mention what type of ichthyosis your daughter has, so if she has LI or CIE, I would recommend you keep her completely out of the sun until this is over. If she has a form of ichthyosis that does better with sun exposure, try to get her a little bit of exposure and see if it helps, but don't overdo it. Keep the exposure time minimized until you know if it helps or hurts.
Making sure she doesn't get stressed is also very important. If she gets upset and if her hives act like mine did, they'll get worse and spread. Lots of naps were also a good idea for me.
I am female, and was born in 1972 with Lamellar Ichthyosis.