I believe it's not a worthwhile strategy to try and eliminate or cure an allergy. Controlling the symptoms brings the best relief. The allergies I have are survivable. This Ragweed season may be the worse ever, but I'm a little better at controlling the symptoms.
About the honey, you'd have to eat a lot of honey and for a long time. Honey isn't cheap where I live.
One solution I've been considering is living outdoors all the time in a city with low pollen counts. The main obstacle is vagrancy laws. :-) Indoors, allergens concentrate and worsen the symptoms (unless you live in a house/apartment with effective filtering/ventilation).
If an OTC antihistamine works, you're very lucky because many allergy sufferers have to get prescriiption strength. Besides, ragweed season is only for a few weeks a year (there's also a ragweed season in the spring, I seem to recall). Here's hoping that next year will be less severe.