Sorry to hear that you got a bad splinter, and that you are having a rough time getting it out. As with any foreign body that punctures the skin, thin pieces of wood (I am assuming the splinter is from wood) can potentially carry bacteria that was on the surface of the foreign body, or drag normal bacteria that is on the skin (called normal flora) down into the deeper tissues and potentially cause an infection. As you are alluding to in your question, this infection can be potentially made worse if you use "dirty" (meaning non-sterile) instruments to try and remove it. After all human skin is the first, and best, barrier that we have to infection. In general I tell people that if the splinter can be easily removed using a set of clean tweezers, then to just pull it out. Most splinters are located in the hands or feet and are easily accessible for this. If there isn't anything to grab a hold of, and the splinter isn't too deep (meaning that you can see the entirety of it through the skin) then a clean needle can be used to unroof the thin layer of skin over top of the splinter enabling it to be grabbed with tweezers. If this doesn't work, and it's not infected (red, painful, draining pus) it may be reasonable to leave it, and the body will typically work it out over time. However if there are any signs of infection, or if it is in a sensitive location, or bothering you significantly, I would suggest making an appointment with your primary care physician
to have it removed (and potentially treat the infection). I hope this information is helpful, and I wish you all the best.