My DH has taken both Claritin and Tylenol, and has a very severe gluten allergy. He's fine with both, so no worries there.
Yes, it is possible to have Celiac with a negative blood test result.
An elimination diet - in which you avoid all gluten - is the best & least expensive way to know for sure.
Also, there is EnteroLab.com
testing. They can look at stool (for giadin antibodies) and saliva (gene test) to determine if you have markers for Celiac. That's how I was tested.
You might look into the Paleo Diet, as it is free of grains and dairy. You can adapt the recipe if it calls for corn or leafy greens, to suit your needs. See paleofood.com/
Chronic Lyme, Bart., Gluten & Sulfite Sensitivity, Many Food/Inhalant/Medication/Chemical Allergies & Intolerances, Asthma, Gut dysmotility & non-specific inflammation, Lupus, Osteoporosis, etc.; G-Tube
Meds: Flagyl, Domperidone, Claritin, Andrographis & other herbs, homeopathy, supplements, etc.