This is a difficult one, because MS doesn’t actually damage the peripheral nerves - e.g. those in your hands and feet, but only the central nervous system (brain, optic nerve & spinal cord).
The reason it feels like nerves in say - your hand - are getting damaged is because the damage in the central nervous system means messages from them are arriving garbled, or perhaps not arriving at all. It’s a bit like if my phone is working perfectly, but I phone you, and you can’t make out what I’m saying, because there’s a fault at your end. So perhaps you end up with a completely wrong message, or can’t make it out at all.
It is possible that a physical injury to the hand, such as botched insertion of a cannula, could cause nerve damage, if you were very unlucky. But this would be completely separate and coincidental from the type of nerve damage caused by MS.
I think it’s more likely that the hand has just been left a bit sore, but because your brain may be getting garbled messages, it doesn’t know quite how to interpret “sore”, so you get some random sensations that something’s not right, but perhaps not the ones you usually associate with injury.
But numbness and pins and needles in the hands are very common with MS anyway (I’m experiencing it as we speak, in my non-typing hand), so it’s possible it’s complete coincidence, and nothing to do with the cannula.
Might be worth e-mailing the neuro, in case it is the relapse she’s been waiting for. But I realise you won’t get in to talk about it, or have any tests, this close to Christmas. Might be worth getting it on the record anyway.