Sometimes I wake up a little dizzy and off-balance. When it first happened to me, I was mortified and panicked about it all day, which made it worse! However, like you, it went away when I woke up the next morning. Now when it happens, I attribute it to sleeping funny (I grind my teeth and contort into weird positions when I sleep), or maybe not eating right the day before. Drinking water and eating light, nutritious snacks throughout the day that I feel "off" helps a lot.
Convincing myself that it's a transient feeling that will pass eventually helps to ease my anxiety. I tell myself "if I can just get through this day, it'll be gone tomorrow."