Can food allergies cause (very intermittent) sharp abdominal pains 2-3 hours after a meal? can food allergies make you feel really run down and tired?

It's possible: Consider a good medical exam and ask about allergy testing. Let the exam cover other possibilities too, since there can be other reasons. I hope it goes well and you find a solution.

Yes but.....: Food allergies can cause abdominal pain, and frequent exposure to food allergens can contribute to fatigue, but (and this is a very strong "but") food allergy is an UNLIKELY cause of your symptoms. Because there are many other causes (some serious, most treatable) of your symptoms, you need to see a doctor about this. Please!!!