Save the complaints about previous treatment for later.
Your daughter presents with a symmetrical response to something...both hands, both arms, and breathing difficulty.
A spider bite...who knows? As Dan mentioned...another bug...a fungus...who knows?
Get to a doctor and have some baseline blood work done - Comprehensive Metabolic Panel, fasting lipid panel, a hemogram, Erythrocyte Sedimentation Rate, C-Reactive protein, a fungal assay, Vitamin B & folic acid levels, Lyme disease and Lupus testing are a good start point. And an allergy work-up. An EKG.
An incidence of breathing difficulty is very troubling. Very.