Go through these in order and stop at the first one that applies. If you are reading this for someone else, answer for them.
Go to emergency care if elbow redness or swelling is accompanied by severe whole-body illness, such as confusion, fainting, marked drowsiness, breathing difficulty, or rapidly worsening symptoms.
These can be signs of a serious infection affecting the body.
Get same-day medical help if the area becomes increasingly red, hot, or painful; redness is spreading; pus or cloudy fluid drains from the skin; or you develop a fever or chills.
These symptoms can indicate infection.
Seek prompt assessment after a significant injury if you cannot move the elbow normally, the joint looks deformed, or you develop numbness, weakness, a cold hand, or severe pain.
Arrange a routine appointment if the swelling is not improving, keeps returning, interferes with movement or sleep, or has no clear cause.
You should also seek advice if you have gout, rheumatoid arthritis, diabetes, a weakened immune system, or take medicines that suppress immunity.
Every sign above is quoted from the sofidex article on Olecranon bursitis. If you are not sure, err upward — it is always reasonable to be checked.