Peanut allergy signs and symptoms can include: 1  Runny nose. 2  Skin reactions, such as hives, redness or swelling. 3  Itching or tingling in or around the mouth and throat. 4  Digestive problems, such as diarrhea, stomach cramps, nausea or vomiting. 5  Tightening of the throat. 6  Shortness of breath or wheezing.