Is sensitivity to wheat/gluten a milder form of Coeliac disease?

No it's not. As soon as you've clarified everything with the doctor and moved to a gluten-free diet, you must stick to it to see positive changes. Gluten/wheat sensitivity is a distant relative with symptoms and characteristics which are very similar to those of Coeliac disease; however, your body produces no antibodies so you must go through everything carefully with your doctor before you start a gluten-free diet.