"I’m curious, does the reaction occur due to the allergen coming in contact with the lips, or is it the digestion that causes it?"
"And how long does it take for it to cause the reaction?"
It depends on how sensitive you are. And, what part of your body has become hypersensitive.
In hypersensitive people, reaction can occur just about at any step.
step 1: You touched food with your fingers/hands (common symptoms of this are often dyshidrotic eczema and contact dermatitis)
step 2: You touched food with your lips (common symptoms of this are often oral allergy syndrome )
step 3: You are chewing the food, and digestion inside your mouth started (some of the food particles have already reached your bloodstream at this point, and reaction may be severe )
step 4: Food is inside your stomach (the common symptoms are stomach pains, indigestion, burping, bloating, gass, cramps, etc )
step 5: Food is inside your small intestines
step 6: Food is inside your large intestines
Some people may react at just one of those steps, other may react on multiple steps.
It sounds like you may be the one that reacts on more than one step.
"And how long does it take for it to cause the reaction? I’m wondering because I notice when I eat things like a sandwich with bread and it touches my lips, my lips usually dry up really fast when I’m eating, and by the time I’m finished the skin looks more dry and peeling."
Instead of asking me, ask that question to yourself: "how long time does it take to eat a sandwich " :-)
"I’m also wondering if you’re a doctor or what’s your background for having so much knowledge in this topic? "
I am not a medical doctor, I am just a guy who is more than average interested in health, and maybe a person who is able to connect the dots and see a clear picture in places where most other people only see random dots :-)
Based on the symptoms you just told me, yes, you are hypersensitive to something inside that sandwich. It may or may not have to be gluten, or wheat, may be chemical additives added to bread before baking.
For your information, 99% of all commercial breads are made with additives produced by chemical industry, additives that your great grandma could never have had in her kitchen!
Many of those additives are never written on the label. How do I know it?
First hand experience.
Some time ago I used to work in a large bakery, and had access to all recipes of all products baked there. Of 25 different breads, 25 had chemical additives not listed on the label, that is beside common ingredients, like salt, yeast, different flours and water.
The same is true for just about any other product of food industry. Beside everything listed as ingredients, there are unlisted ingredients, and those may play a major role in hypersensitive people, as those chemicals are not food and are not intended to be consumed.