Ok my gut feeling and I could be wrong is that you might not have a splinter. You might have a plantar's wart. And while pedicures can be very pleasant, nail shops or beauty salons are probably not the places you want to go to get even a splinter removed. Standards of cleanliness vary wildly and I can tell you from experience that even in the cleanest of them, fungal and other infections are very common in these places (please take it from me.) And believe me, you don't need a foot infection on top of anything else.
My advice? Go to a podiatrist, my friend. Ask around, find someone's who's good and go. No mattter what it is, they are the ones to treat it.