<<Disclaimer:  Verify this information before applying it to your situation.>>

I am sorry to say that your doctor is incorrect.  Celiac Disease is not a
group of allergies at all.  In fact, you will probably be receiving many
messages to this effect.  Celiac Disease is a malabsorption syndrome whereby
consumption of gluten containing foods flattens the villi of the intestine
making absorption of nutrients from all foods next to impossible, and it
leads to a whole host of problems, from anemia to malnutrition.  Your
"allergies" seem to be a seperate issue.  If indeed you do suspect you have
Celiac Disease you should see a gastroenterologist who has sufficient
experience with this syndrome, be properly tested for it, and, if indeed you
do have it, adhere faithfully to a gluten free diet.  Coincidentally, you may
find that if this is the case, and you do follow the diet religiously, many
of your other "allergies" may go away, as evidenced by many of the postings
on this list.
Good luck!