Are there complications associated with tooth abscess that has drained?

Yes: Tooth must be treated either by root canal treatment or extraction. If not, the cause of the infection will not be treated, and you will reinfect. Draining helps treat the symptom, but not the cause. Get treated asap.

Yes: There was so much infection and pressure from that infection that it pushed out the soft tissue. It will not be fixed until the tooth that is infected is treated. It could need a root canal an extraction, or possibly periodontal treatment.

In short, yes!: A tooth abscess is not something you want to self-treat....Safely. These can become very serious. Please seek professional care from a dentist immediately. These infections spread to other parts of your body and can be very damaging.