Hello,
Thanks for posting your query.
There are various causes of dry eyes apart from dry eye syndrome which as your doctor said is rare in children.
In addition to an imbalance in the tear-flow system of the eye, dry eyes can be caused by situations that dry out the tear film. This can be due to dry air from air conditioning, heat, or other environmental conditions. Other conditions that may cause dry eyes are:
The natural aging process.
Side effects of certain drugs such as antihistamines .
Diseases that affect the ability to make tears, such as Sjogren's syndrome, rheumatoid arthritis, and collagen vascular diseases.
Structural problems with the eye lids that don't allow them to close properly.

Depending on the cause the treatment includes lubricating eye drops , steroid eye drops or surgery.Though there is no cure in many cases removal of cause provides adequate relief and lifelong treatment is not always necessary.
If your child has been suspected of dry eye syndrome it's best to confirm the diagnosis by tests like schirmers test by your eye specialist before any management is decided.

Let me tell you something about dry eye syndrome.
Dry eye syndrome is a disorder of the film where tears are normally produced. When dry eye syndrome occurs, the eye is incapable of producing a sufficient amount of tears, or the tears are composed of chemicals that cause them to evaporate immediately.Other causes for dry eye syndrome include prolonged periods of eye-heavy activity, including watching television, reading or using a computer, dry or dusty air, other medications, or prolonged contact lens use.
Patients with dry eye syndrome often report persistent eye dryness, a sensation of burning or scratching in the eye, blurred vision, a gritty or filmy feeling in the eyes, light sensitivity, and eye redness or "foreign body sensation".

To be certain the child suffers from dry eye syndrome, a physician will likely order a Schirmer test, a procedure which attempts to measure the amount of tears in a patient's eye using a thin strip of filter paper placed at the corner of the eye.

Pediatric dry eye syndrome can be treated by lubricating or steroid based drops as advised by your ophthalmologist.Some measures may provide some relief like massaging the child's lids, cleaning the eyelid margins twice daily with diluted baby shampoo (approximately one teaspoon of shampoo to one cup of lukewarm water), refraining from medication that may be causing the eye to dry out and ensuring your child consumes the necessary amount of Vitamin A and essential lipids. However these should only be done after consulting your eye surgeon.

So please don't worry, and I hope that with appropriate intervention your child will have a speedy recovery .
Hope I have answered your query.
Kindly accept my answer if you have no further queries.
Regards

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