A more appropriate word for feeling "high"?

Euphoria, or in this case euphoric.

You could say that the person is one of the following:

• feeling alive
• in high spirits
• in good spirits
• lighthearted
• upbeat

What about "feeling elated"? According to the Oxford Dictionary, if means "very happy and excited because of something good that has happened, or will happen".

or else "ecstatic", which in the same dictionary is defined as "very happy, excited and enthusiastic; feeling or showing great enthusiasm". In this meaning, it is said to be a synonym of "delighted".

I admit that they all sound a bit stiff and old-fashioned.

The previously-suggested words euphoric, elated, and ecstatic all are good, but don't overlook exhilarated ("refreshingly thrilled") and exuberant ("high-spirited; extremely energetic or enthusiastic").

It's going to be hard to displace a natural and well-established Metaphor like the UP/DOWN family of metaphor themes.

Being metaphorically high, for whatever reason, and in whatever way, is coherent with the

• UP is HAPPY (DOWN is SAD) theme
  • He’s depressed.
  • feeling up/down
  • What a downer!

as well as the

• UP is BETTER (DOWN is WORSE) theme
  • He fell down on the midterm.
  • a rise/fall in performance
  • upwardly-mobile

and the

• UP is ABSTRACT (DOWN is CONCRETE) theme
  • head in the clouds
  • feet on the ground
  • Come back to earth.
  • new heights of abstraction

Virtually all the ways we use to talk about mental experiences are metaphors. Nothing new here.