Tennis Elbow is typically an overuse injury combined with poor technique / posture. I find two areas of injury , tennis itself and from using a mouse ( typically in hypermobile patients).
I focus on relieving the muscles around the injury and getting the inflammation down on the sensitive area of the elbow which is often tender to touch.
Short term relief suggestions.
Ice little and often (5 minutes on 25 minutes off) . If the injury is from tennis , you probably need to rest it. If from working with a mouse, get a wrist support and take regular breaks and ice too.