Yes ma'am, food allergies can manifest in form of rashes. It may not necessarily be food, one can also be allergic to water.

RECURRENT NASAL DISCHARGE aka running nose in children is ALLERGIC RHINITIS.

Signs of allergy includes Rashes, itching, nausea , vomiting, diarrhoea, abdominal pain, cough, swelling on the body etc are all signs of food allergy and/or intolerance......Food allergy is worse than the intolerance"...For treatment kindly avoid food you suspect are responsible for the allergic reaction. Kindly visit the hospital if persistent or still concerned

Groundnut is essentially what is in the peanut butter. As long as the child is not allergic to groundnut. Give a little to taste first and observe any reactions before giving more'