Red swelling under third toe

Please understand that your question is no more answerable than had you perhaps asked, "Why do I have pain in my eye?" You might have your symptoms for any number of reasons, but a simple recitation of common symptoms and findings such as pain, stiffness and swelling in the foot leads to no more meaningful conclusions than would similar symptoms anywhere else in the body without a detailed history and an all-important examination. That being said, pain, redness and swelling are common signs of infection and this should be ruled out professionally.