Yes, this is a skip-level discussion. Don't threaten to leave, or anyhting. Just patiently ask why you're not getting feedback (written or verbal) on why you didn't get a raise. Make it clear you're interested in learning precisely what you need to do to qualify for one.

If at that point they dont' give you actionable feedback, get a competitive job offer and share it with the head of HR at your company along wiht a short note saying that you can't afford to keep working there.