Word for person who is always dizzy or high
A person that is dizzy or high WITHOUT drugs might be described as "giddy."
(But maybe the associated adrenaline is a "drug.")
If you want to refer to someone who is always on drugs, you can call them a stoner. This primarily refers to someone who uses cannabis (marijuana), but you could apply it to mean anyone on drugs.
A more formal term is addict:
a person who is unable to stop taking harmful drugs
If you wanted to be clever, you could describe someone who is always dizzy as vertiginous. This is how I describe myself when having bouts of vertigo.