What if my job genuinely doesn't allow it?
Then build the smallest real version: one protected evening, or a half-day. A protected four hours beats a theoretical full day you never take.
Does a day off mean doing nothing?
No. It means doing nothing you owe anyone. Long hikes, cooking, and building things all count; unanswered obligations don't.
I feel guilty and anxious when I rest. Is that normal?
It's common, and for most people it eases as the day becomes routine. If rest reliably makes you anxious rather than restless, that's worth raising with a professional rather than out-stubborning.
Should the day be the same day every week?
Ideally, yes — a fixed day is far easier to protect and easier for other people to plan around. A moving day tends to move until it disappears.