Gout in humans starts with one and quickly goes to the other. It is a chronic condition and managed with starches. Meat makes it worse. It is inflamed when you have a lack of these in your diet and is caused by acid in your joints. So, no I do not think it is gout. It may be arthritis, which can present in one or many joints.
I don't know for sure what the problem is, however I do have a suggestion for treating the symptom. Try a warm Epsom salt bath for the foot. Epsom salt reduces swelling and draws out infection if there is any. Reducing swelling can help with pain. Also, with less swelling you could feel if there is a noticeable injury.