The simplest way to know whether you have food allergy or not, is keep a food and symptom log. Log in whatever you eat and the swelling as it appears and see if there is a correlation.
The other possibility is that the neck swelling is an exacerbation of the GERD or gastric reflux. It could also be hiatal hernia. Treatment is a combination of drugs to reduce the acid and lifestyle changes. You will need to take a combination of medications (under medical supervision) like a proton pump inhibitor such as omeprazole, lansoprazole or pantoprazole empty stomach in the morning and an antacid gel after meals or H-2 blocker such as ranitidine for complete relief. Possibility of H pylori infection too should be looked into by a carbon urea breath test and a combination antibiotic tried. Many a times a persisting H pylori infection can be the cause behind acidity not responding to treatment.
Life style changes that will help include: Drink cold milk. Avoid heavy meals and eat frequent small meals. Avoid too much of caffeine, tea, smoking, fried food and drinks both alcoholic and non alcoholic fuzzy ones. Avoid heavy exercises within 4 hours of a heavy meal. Raise the head end of the bed by pillows to 30 degrees. Avoid lying down for least 2 hours after food. Take a late night snack. Maybe these tips will help you. Take care!
The medical advice given should not be considered a substitute for medical care provided by a doctor who can examine you. The advice may not be completely correct for you as the doctor cannot examine you and does not know your complete medical history. Hence this reply to your post should only be considered as a guiding line and you must consult your doctor at the earliest for your medical problem.