Mildy infected splinter site

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I got a large thorn just under the skin on my finger whilst gardening yesterday.

After much poking and prodding I got most of it out but suspect there's still a tiny fragment there.

This morning it's red and sore and there's some pus. I'm well in myself and it's only the immediate site of the splinter.

This is OK, right? It's just the healing process? It's just you hear such awful things abiut sepsis taking hold so quickly.

Bathe with salt water? Anything else?

Put some savlon on it and a plaster. For now, keeping it moist will help it come out. I know some people will come on and recommend mag sulph paste, but I've never tried that myself.
Obviously, if it starts to look angry, draw a line around the redness to see if it's developing further and if it does, contact your GP for some antibiotics.

I'd do the bathe with salt water, cover it with a plaster and then stop fretting xxx