Right on the tip of the elbow? (The Olecranon).
You've probably irritated the bursa (sac of fluid that protects the inside of the skin from the bone etc.).
One of mine inflamed and the doctor said it was off leaning ("Student's Elbow", "Drinker's Elbow" etc.) but I hadn't lent on my elbow for months due to another problem with it that did require surgery. The surgeon told me that they can inflame for other reasons (I was getting worried thinking that my elbow problems were linked but they weren't).
Doctors seem a bit reluctant to remove or drain bursae, you can grow a new one if it is removed (would that be reimbursement? ). Bursae (I think that's a proper word!) are susceptible to infection so they leave them alone.
Mine took a few months to settle down. Sometimes it felt like I had a bit of gravel in my elbow. Do you have a bump there?