I have swollen hands and severe pain after playing tennis. what can i do?

A lot of things : Swelling of the fingers is usually related fluid building up. The causes include; arthritis, carpal tunnel syndrome, tendinitis, vascular outflow issues, inflammatory conditions and infections. Once the cause has been identified an appropriate treatment plan can be established. It sounds like tendonitis after playing tennis. Good antinflammatories and soaks with epsom salts.