What are some causes of swollen eyelids in a 14 month old child?

Many. There are many causes of swelling eyelids, including allergies and infections, bug bites, sinusitis, trauma, and just rubbing the eyes too harshly. However, there are rare things that have to be ruled out like tumors. Its always a good idea to see an ophthalmologist if there are unexplained eyelid swellings.