Poorly big toe but won't let me near it

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My dd (16 months) has something in/on her big toe underneath. I noticed she winced then cried when I touched her foot the other day but on closer inspection today, I can see there is something in it and it looks red/raised so probably infected? Could be a splinter perhaps. Is it normal to have 'bits' from the carpet ingrained in to the skin?

I'm going to the GP tomorrow, but thought I'd check if any one has any experience of this? She's going to scream when I have to show the GP - will he try and get it out or prescribe antibiotics?

Pressed send to soon. We've tried to look closely today and she's really distressed even just touching her foot/toe, like she's really in pain.