If you are not 100% sure all of the splinter is out, you really should have it checked out. In the mean time, soak the finger in warm Epsom salt water several times a day. This will help draw out any pus/infection. Keep the area clean. But if you are not sure if the splinter is all out, or if the above doesn't help, do be seen.
There is a cream called Ichthammol, which you can get at your local pharmacy. This cream is a drawing out suave. Generally you will apply this cream, cover with a band-aid and it helps draw infection out and if you still have a splinter left, it can draw that out too.
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