To hit the back without rows or pull ups I would to a comibination of:
-Band pull aparts
-Reverse flies using cables/machine
-Straight arm pull downs using a cable and lat pull down bar OR pull overs (dumbell or barbell)
This way you will still hit the upper back with the 1st two movements and also hit the lats with the straight arm pull downs/pull overs, but non of the movments involving flexing at the elbow so they shouod be fine for you.
I used this when I had biceps tendonitis and also couldn't row/pull up and it maintained back size and shouldr health pretty well.