Yes, allergies can cause fevers. I get fevers from certain things I'm allergic to. Have IBD, Lupus, and other chronic inflammatory disorders been ruled out (chronic low-grade fever is a common symptom in most of these conditions)?
Gluten & Sulfite Sensitivity, Multiple Food & Inhalant & Medication Allergies, Asthma, Gut issues (dysmotility, non-specific inflammation), UCTD (Lupus?), Osteoporosis, Anemia, Very Low Lymphocyte Counts (T-Cells & B-Cells), malabsorption/malnutrition, etc.
Meds: Pulmicort, Injectable Vitamin B12, Herbs, Nutritional Supplements, Essential Oils, Homeopathy.