Is it possible for seasonal allergies to cause loose stool and skin irritation in a 2 yr old?

No and yes. The loose stools are not a typical response to seasonal allergies. If the 2 year old is producing lots of mucous because of allergies and swallowing it his stool could become loose. The skin reaction may be an associated symptom of allergies. Discuss with your doctor appropriate medication or other treatment for a 2 year old.