This is an unusual problem. It is not common that people experience problems as you are decribing. While this may be minor, I would recommend that you discuss this with your primary care physician. In addition, a gastroenterologist
(a food / stomach specialist) as well as an Ear - Nose - Throat Doctor
(more commonly known as ENT doc) would be helpful. Talk to your primary care doctor
who could arrange you with the aforementioned specialists if required.
Fundamentally, a sneeze is a way the body removes inflammation and congestion from the nasal passages. Much like a cough keeps the airways clear, a sneeze is a reflex to keep the nasal passages clear. As such, sneezing after meals suggests that there is some cause of inflammation that occurs after each meal. As for what is causing the inflammation, you are right in thinking allergies are the most common cause. Common food allergies such as egg, peanut, etc should be ruled out. It sounds like you've already done that. There is also a possibility of mechanical inflammation, that is a problem with your swallow reflex that is causing food to irritate the top of the nasal passages. An ENT can evaluate this. Also possible is the food is causing a reflux of stomach contents that is inflaming the nasopharynx. This more commonly causes a cough, but could possibly cause sneezing.
See your primary care doctor. Good luck!