Nasty looking splinter

[Buddyelf]

My dd (just turned 3) has a splinter I noticed this morning. It's on the palm of her hand and looks deep. I can't feel an edge and it looks really red.
She is throwing a serious tantrum whenever I go near it, I have no idea how I am supposed to get this out before it gets infected?
I don't think I can do it in her sleep - she'll wake. I've tried holding her down but DH is in work and I don't have enough arms!
Realistically if I can't get this out and it's looking nasty is this a GP visit, walk in? I'm worried it's going to get horribly infected.

I asked a similar question on here a week or so ago and magnesium sulphate was recommended and it worked. I was amazed. Slathered it on the splinter each evening (was on DS' foot), put a plaster over the top and it just came out after about a week.
BUT at no stage did it look inflamed or infected. It was deep and big and a bit red but that was it.

Olive oil works quicker than magnesium sulphate. Put it on and cover with a plaster should come to top after a couple of days.