The toe next to my big toe is red swollen and painful to touch. arthritis or infection?

Infection: Yes it could be an infection. Less likely arthritis or gout. You need to get it checked.

I suspect arthritis: This type of involvement suggests a dactylitis, and the most common cause of dactylitis can be psoriatic arthritis. It can be something else and it depends on what joints are involved. But if the whole toe is swollen and not just one joint i suspect dactylitis. You need evaluation because we have therapy for this or if it is something else other appropriate therpay would be directed.