Are there autoimmune disorders that causes red, swollen, inflamed and itchy eyelids and a rash?

See below: Dermatomyositis can certainly do this.

Atopic Dermatitis: Atopic dermatitis, an immune/allergic disorder, can produce eczema on the skin, as well as red swollen itchy eyelids, and a rash. However, a simple contact allergy, unrelated to an immune disorder can produce similar findings. See your ophthalmologist and perhaps an allergist as well to look into it.