Looks like a group of splinters on my finger that are hard to get out? What could this be?

Well it is difficult to say what these are without physically seeing them. This does not sound like plantar warts. It is possible that they are really just splinters. There is something called splinter hemorrhages, but they tend to occur under the nails and this is unlikely the cause of your lesions. You should check with the doctor if these are still present and you are unsure the cause. Unfortunately I cannot suggest any treatments without knowing the cause. Most likely this is nothing serious and will resolve with time.