sounds like a blackthorn/sloe, expect a red finger for a couple of days!
my mum always said removing splinters/stitches/sticky plasters, infact anything you are trying to remove, is always easier after a bath (skin is softer).
you could improvise with warm damp cloths, or keeping a hand immersed in warm water.
you could use a plant like Dock leaf to make a warm poultice which may help soften the area.
sometimes it is easier to do away with tradition and use a needle or shape blade to cut a larger hole then the evacuation is easier (but obviously much more prone to infection) perhaps not a good idea if clean items are not available.
Of course there is the
grin and bear it way, within a few hours of there being an alien body in your finger the bodies defences are set to kill it., often the splinter will be eaten, or moved by your body's defences.
I think it's fairly common knowledge about people finding bits of metal glass etc in strange parts of their body ages after they've had an accident.
the body is amazing and will sort it out if we dont
) and poulticed on the festery bit.........works quite well under a plaster of bich polypore 
) I just cut a tiny slot with the tip of the mora knife and it burst open, a small amount of thick pus emerged and the splinter as well. I find sometimes you just have to leave them to there own devices, you can pick about with needles etc but some splinters (I think this one was oak, I get splinters all the time and often forget I have them) are very clingy and stubborn and it makes it worse. A mate of mine used to get lots of metal splinters in his hands. He swore by a simple remedy-soak your hands in hot water for a few minutes (or wait till you had a bath) then rub olive oil onto the hands. They pop out over the next few hours 9the splinters, not your hand's 
