Yes, it is possible for a 2-year-old child to have seasonal allergies. Common symptoms include runny eyes, sneezing, and a runny nose. To help alleviate these symptoms, you can try giving them Claritin syrup once a day for 3 days, which is available at the pharmacy. If the symptoms improve with this treatment, there is a high likelihood that the child is experiencing allergies. It is important to make sure there are no signs of infection before treating for allergies.