How do I get rid of a blood blister next to my tragus piercing. It doesn't hurt and isn't infected, but it just looks gross. I want it to go away.

Chronic irritation. The tragus is composed of cartilage which gets it blood supply by diffusion. It is prone to an infection, and this could be an infection without purulent material. Constant irritation could make it look like a blood blister. It would be best to remove the piercing to get the tissue to heal. Clean the site with saline, apply antibiotic ointment every eight hours, and do not pierce until healed.