fungal nail infection in newborn

[StuckOnARollercoaster]

I have a 13 day old baby and she has a sore finger. Her nails have little bits of loose skin on the sides and on one of her hands the index finger is starting to look red and sore.
I showed the midwife yesterday and she said it's probably a mild fungal infection and is fairly common. I should put sudocrem on it and ensure its in a scratch mitt, but if not better by Monday I should take her to a gp.
I've done a MN search but on my mobile so hard to see if there have been any other posts on this. I was wondering if there'd anything else I could do? As an adult I'd probably add a drop of lavender oil but would it be too much for a newborn to wash her finger in cooled boiled water with a drop of lavender oil?
Thanks...

Just bouncing in case this rings any bells with anyone?
Thanks

I have been using virgin coconut oil on my own fungal nail which seems to be working well so that might be an idea as it's a gentle, natural product. I also use it for ds's occasional sore bum.

To be honest, with a newborn, I would do what the midwife suggested.