Eyes problems can lead to permanent vision problems in dogs. There are many factors which can cause your swelling in the eyes of dogs. Most common cause of periocular swelling in dogs is allergy to toxins of insect bite. Inflammation of the conjunctiva due to bacterial or viral infection is another cause of eye swelling. Some foreign bodies like splinters or grass in the eyes can also cause eye irritations leading to eye swelling. So, it will be ideal to take your dog to vet.