Which doctor should I see for persistent dizziness?

For the past week or so, when I get out of bed in the mornings, it literally feels like the world is collapsing on me. Everything spins for about ten seconds and then it passes, but I still feel dazed. During the day, sometimes I feel like I'm falling into this void. I’m not sure if my blood pressure is low or if it’s something related to my ears. Should I go to the internal medicine specialist or just go directly to the ENT? Which one would make more sense? I don't want to be wandering around hospitals unnecessarily.