Yes walking is good also.
On the occasional mornings when I awake stiff or sore from sleeping wrong, walking always loosens me up. Always.
Not sure stairs are good for you when you are this acute but definitely when you are feeling less pain, IMO.
Another really helpful and important thing-keep your abs tight/contracted constantly. This will help support your spine which is really needed right now.
Over the years I have gotten really strong abs which helps me.
When you have a spine injury, the muscles are traumatized and of course so sore they cannot support your spine/body without horrible pain and so other muscles have to take up the slack.
Your glute muscles and legs will/have taken over, so remember to gently (go slow!) stretch them out daily; massage will also help. Don't forget to massage down to your lower your legs too, as everything is connected and they will get sore too.
If/when needed I take the gel caps of Advil (actually the Costco brand Kirkland). The gel caps seem to work better for me than the brown hard tablets for some reason. I am sure herbal refreshment will help too.
I know you have gotten a lot of good advice. I just hope you feel better soon.