Ripped lower back muscle- climbing the walls with boredom!

I have recently ripped my lower back muscle (where it joins the spine at the base) and am on some rather nice pain killers as a result however; I am also bored out of my mind and missing my phys' rather badly. Are there any suggestions for some upper body workout exercises that I could do which shouldn't affect my back? (Doc says I can start spin classes and or swimming next week as long as I take it gently for a week or two, to keep my cardio training up). Thanks in advance :)

Edited to add; probably a stupid question but as I will be suspended and it would work mostly the upper back (in my very limited knowledge of the muscular system), could/ should I attempt overhand pull-ups?

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