What could cause red / swollen toes?

Many things: Inflammatory arthropathies like rheumatoid or psoriatic arthritis, trauma, gout (though usually in one joint.), tight shoes. Is it only the toes that are swollen? Either way sounds like a visit to the doc is a good idea.

Many reasons: You could have infection, inflamation, arthritis, auto immune disease, vascular problems.These are some reasons there are many more.

Several: Certain condition can cause this such as raynaulds phenomenum. This is a benign condition of spasms of the venous/end arterioles of the digits. Cold and stress and smoking are triggers.

Many possibilities: Some causes of swelling can include systemic problems such as hypertension, and problems with the kidneys and localized issues such as arthritis, infection, lymphatic obstruction, blood clots, varicose veins, trauma (fracture, sprain, tendonitis, tight shoes) and side effects to medication. Have it evaluated by a professional and get the appropriate treatment.