It looks to me as if you do not have celiac (double check with your doctor, ask directly!) , but you can still have a sensitivity/intolerance to gluten.

People with celiac react to microscopic exposures to gluten. Cross-contamination is an issue. People who are sensitive/intolerant need to avoid gluten but in my experience don't have to be careful to the extent that people with celiac do.

My daughter has celiac. She has her own set of pans etc. I am gluten-sensitive and just wash mine!