It is not highly unusual for your nose to run when you are eating. If it is running heavily and bothersome to you, then you can consider a food allergy and either visit an allergist or you can try taking an antihistamine, if it is not contraindicated for you, and see if this controls the allergic reaction. Concerning the dry skin and scalp that you are experiencing, be sure that you use a shampoo that has a moisturizer or conditioner in it. Do not wash your hair more than two times a week so that you do not wash the natural oils from your scalp. Apply a moisturizing cream or lotion such as eucerin or aloe vera behind your ears. If this does not help then you will need to be seen by a dermatologist for evaluation.
You are welcome, George. Please let me know if you have any further questions.