What's the word for a tiny sharp piece of wood under your skin? [closed]

When you work with crude wood (or iron) without gloves, you easily get injured with a tiny sharp piece of wood which remains under your skin and needs to be removed.

What is the word for this small piece of wood used in that particular case? I've found several words in the dictionary but without the collocation: splint, splinter, sliver.

And what is the whole phrase for the injury? Something like to get a splint?

I think that you can use splinter regardless of the material. In Merriam-Webster's Unabridged Dictionary online (subscription required), the example sentence for splinter in the meaning you intend references metal.

splin·ter
noun \ˈsplintə(r)\
plural -s
1 a (1) : a thin often jagged or needlelike piece split or rent off lengthwise : sliver, chip, fragment

gloves … protect a worker from sharp steel splinters — Michael Cawley
the steering wheel … was knocked into splinters by an enemy shot — Edward Breck

(2) : a small jagged or needlelike particle or flash

flying splinters of ice — William Beebe
irradiated for a moment now and then by splinters shooting through the darkness — E. K. Brown

And I think sliver is an acceptable synonym for splinter in your use. Here's the definition for sliver from the same source:

sliv·er
noun \ˈslivə(r)\
plural -s
1 a : a long slender piece cut or torn off : splinter

a piece of apple pie with a sliver of cheese on top — F. C. Othman
was building up the fire with split logs and pine slivers — William Faulkner

Neither of these words refer to the action of getting a fragment stick under the skin, so in formal use you would have to specify: "Last time Bob tried whittling, a splinter stuck in his finger, and he couldn't get it out for days." But when the use is informal, I don't think it's a problem to imply the action: "Ow! I just got a splinter!"

It's called a splinter in the case of wood. "I've got a splinter in my bum from sliding down the bannister". Splints are something else.

That's because wood can break apart (splinter) into sharp bits. In the case of metal, I'd call it a metal cutting, a chip, a shaving, a sliver, or a piece of swarf.

In the case of glass, I'd call it a sliver or a shard.

There is an uncommon but a more specific word: skelf.

a splinter of wood, esp when embedded accidentally in the skin

_{Source: http://www.thefreedictionary.com/skelf}

It is from Scottish English and used as a slang mainly. You can encounter in literature too.

Also, spell and spelk is used as a splinter of wood but they are more of a dialectal word and uncommon.

Note: This would be a supplementary answer to Sphero Pefhany's answer. He already mentioned the most common usage in his answer.