Allergies and sensitivities to foods usually show up as digestive distress (nausea, vomiting, cramping and urgent diarrhea), puffy red watery eyes, stuffed sinuses, and less often a rash that appears on the face (around the mouth and chin especialy, looks like tiny pimples), over the chest and hands. Severe food allergy, such as to peanuts, can cause extreme breathing difficulty, requiring 9-1-1 emergency.
The other thing about true food allergy is that symptoms usually appear fairly quickly, within an hour of ingestion -- and then ease off and ultimately disappear as the offending food is eliminated from the body.

A persistent itchy rash is more likely caused by a contact dermatitis, as NNNorma suggested. Detergents, soaps, etc.... However, an often over-looked cause is NOT ENOUGH FAT in your diet, and I'm referring especially to the unsaturated fatty acids found in good vegetable oils such as olive, safflower and flax. These oils are zero carb, and are absolutely vital for your skin and hair -- that's why they're called ESSENTIAL fatty acids. If you use bottled lowcarb salad dressing, try mixing an extra Tbsp of olive oil into it before you pour it on your salad. Add a couple Tbsp ground fresh flax seeds to a protein shake, if you use those. Make your own dressings with lemon juice, olive oil and herbs for dipping strips of cold cooked chicken or leftover steak. This might not be your problem, but it is something to think about ...

Home remedy - put a half-cup of raw oatmeal flakes in an old pantyhose leg or sockette or whatever. Tie a knot in it, then put this in your bath water. The colloidal proteins in oatmeal are very soothing. If you take showers, don't use too hot water. I've never tried using it in the shower, but I imagine you could use the oatmeal ball and just rub it over your skin.

Take care, hope this helps

Doreen