Hello there,
It seems that you have an inflamed bursa covering the elbow joint (called a
bursitis). A bursa is a small fluid-filled sac which acts as a protective cushion for your elbow joints. An inflammation of this fluid-filled sac can be caused by a (reaction to) a bacterial infection,
injury or due to prolonged pressure on the elbows (also called "Student's Elbow" among students!)
It is possible that, as a physical reaction to the infection you have had after the blood draw, your bursa became inflamed, but without signs of a bacterial infection. That means there is luckily no bacteria involved. A bacterial infected bursitis is usually associated with pain,
redness, and tenderness of the elbow, which is not the case in your story.
Don't worry, your doctor is right. As long as you do not feel pain,
fever or tenderness of the elbow it's okay to just wait and see. A bursitis normally can take up weeks to months before it subsides.
Good luck!