Gum is okay - just be careful with sf gum - can have a laxative effect...
Look - the desire to chew all the time - that is something that needs to be addressed on its own. She doesn't need to eat to chew. Something she should be aware of is that if she is chewing a lot (this would be something she likely does for sensory input - like when she is stressed) is the potential damage to her teeth. I would suggest that when she can (like not in a totally public place) she chew on something called a "chewy tube" These are developed for Occupational THerapy purposes and used for stroke patienets to regain jaw strength - also young children with sensory integration disorder - but I have, on occasion, snagged my son's to use instead of grinding my teeth... it is designed to not damage your snaggles.
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As far as eating all the time - well - I think that something like the three hour diet would help her since the idea here is keeping one's blood sugar stable. DOing so will make her less hungry. If she is just eating mindlessly - either it is a sensory thing as mentioned above or she needs to address whatever emotional issues she has and learn to deal with them without using food as a drug. Food is fuel, not medicine.
Oh - and be areful with carrots - they are relatively high on the GI scale - good snack, but we all know too much of a good thing is still too much, right?
