SI joint pain, but is this a mechanism?

Unless you are a young woman who has just had a baby or you've had a fall on your pelvis, the SIJ is actually a very strong joint and it would be unusual for it to flare up with the type of activity you describe. What is the more likely culprit is the lumbar spine...having to work in a slightly flexed position, this can cause quite a strain on the lumbar spine which can refer pain to the SIJ. As far as calling in...it's your call. However, this probably should have been reported as a work related incident. If you do go to work, I'd probably recommend actually kneeling in the bed behind them with a pillow between their back and your front. Keep your back straight and just use your body weight to keep them upright. You'll probably want to wear an isolation gown to prevent your clothes from becoming contaminated, but I find this position is much easier to work in rather than trying to stand behind and lean forward.