Any advice to relieve pain for tennis elbow excluding medication?

Therapy: Physical therapy, transverse massage, tennis elbow braces, rest, and cortisone injections (assuming you were referring to oral medication).

Ice: How about use of ice and use of a tennis elbow strap. Also strengthening of the forearm and proper tennis racket/ equipment is very important.

Injection: Steroid injection for acute cases, platelet-rich plasma injection for chronic cases. Also, the Tenex (guanfacine) fast procedure done under ultrasound guidance is a new and minimally invasive procedure that can actually "cure" the problem.