My elbow keeps swelling up then it goes down then comes back why is that ?

Olecranon bursitis: Its the joint fluid between bones inflammed. Use simple support brace, antiinflammatory meds if safe for u, avoid extra use and pressure for 2 weeks, see dr if not improved or worse.

Get it checked: Swelling about the elbow without a specific injury could be inflammation or infection. If resolving on its own, unlikely infection. Common things include olecranon bursitis. Best to be seen and evaluated by a physician if this persists, and further tests may be needed.