If your doctors don't know of this, how do you?  Who is the "they"  who
are advising you about foods to add?  "Gum" is both a food substance and a
snack,ie. chewing gum, which is your concern?

If the idea of this allergy existed in one prson's conception and was
untested then it is questionable as having a clinical reality.   I assume
that there are symptoms which led you to consult him and these might be
the more useful level to consult other doctors and not at a level not
demonstrated.  If by gum you mean insoluble fiber/starches, then do a
google using "insoluble starch" as search terms.  These don't get digested
or not well and are useful to people who want to control the amount and
speed of carbohydrates entering the blood.  They remain in the gi tract
and are passed in large part.  Some actually help in cholesterol control.  
The google will show which foods contain them.  What symptoms are your
concern in this question?