Get Your Dog Care Questions Answered by Experts
What you are most likely seeing is a ear hematoma. A basset hound has floppy ears and nearly all of them are affected by ear infections and irritation at some point in their life. Usually chronically. A ear hematoma is actually a pocket of blood usually caused from excessive shaking or scratching and a blood vessels ruptures causing the area to fill. The most important thing you need to do is find out the initial reason this happened. She most likely has an ear infection and get that problem treated.
For the ear hematoma you can do one of two things. Have it treated or don't have it treated. The preferable route is to have the area drained usually surgically. There is a product the veterinarians may have called an ear hematoma system (original name huh?). The product is applied while the animal is sedated. It contains two pieces of flimsy plastic/rubber material applied to either side of the ear with multiple plastic tacks. It keeps the area draining and does not allow it to refill. It must stay on for a long period of time and has to be removed by your veterinarian. Another option is a cannula which creates a constant drain but doesn't always have the same desired effects.
If nothing is done the blood vessels will continue to fill the area, creating a balloon effect. Eventually the vessels will clot but may rupture again and again with head shaking and scratching. The area will scar in and her ear may look deformed and crinkly. I would definitely determine the cause of her head shaking/scratching and resolve that issue or you may end up with two fat ears.