Homeopathic remedies only work via the placebo effect; which isn’t nothing, but not enough to be significant. It’s literally the power of positive thinking.
And they can certainly be harmful, because they sometimes are applied via methods that can be harmful, or include an ingredient that can be harmful (like the Zicam that was infamously causing anosmia before it was pulled from shelves and reformulated). I’m going to speculate that if it’s something homeopathic causing his hand to swell and discolor, it’s not harmless.
(It can also be harmful if people choose not to take medicine that can actually help because they’d rather use homeopathic remedies with no medicinal value.)