I have a history of traumatic brain injury and am experiencing dizziness when laying down. Is this a transient ischemic attack? Could this be a tia?

Unlikely. If it only happens with laying down, it is less likely to be a tia. That being said, if the dizzines feels like spinning and is associated with weakness, numbness, difficulty speaking or seeing, you should talk to your doctor, this could be a tia.
Likely, not a TIA. Positional dizziness is not usually related to a stroke or stroke like symptoms. A specialist in ENT would be a good first choice to investigate the cause of dizziness as you describe.