Oh, yes. As you guessed, many repetitive injuries are still associated with professions that were around long before computers: Tennis elbow sounds like something only members of the local country club would get, but is actually very common among carpenters, plumbers, and truck drivers. In fact, the name Carpenter's Elbow is still heard some today for the condition. Likewise Bricklayer's Shoulder (for bursitis in the shoulder) can still turn up, while Stitcher's Wrist seems to be dead.

But we can go back to an even older occupation! De Quervain's tendonitis, which is pain due to swelling in the sheath where the tendon for the thumb passes through the wrist, is colloquially called Mother's Thumb in some circles. There are many good reasons why it is probably more common among new mothers today (more large babies, more older mothers, and, yeah, more thumb typing on cell phones on top of the stress of cradling an infant), but there certainly weren't cell phones when Fritz de Quervain described the condition in 1895 (although he in fact did not claim this credit).

As for the history of repetitive stress injuries as an overarching idea, I am less knowledgable, but I can tell you that the man recognized as "the father of occupational medicine", Bernardino Ramazzinni, published his observations on workers' injuries at the start 18th century. You can read a good review of his work here.