I've worked in orthopaedics for 16 years, and while I'm not a doctor, I know quite a bit about hand injuries. Numbness or cold is common with swelling and bruising. The fact that you can feel the tip of your finger is a great sign that the blood flow is intact. However, you likely fractured (broke) your finger, and that should be treated by a professional to reduce the risk of arthritis and future range of motion issues. Xrays should be taken to evaluate the bones. In the meantime, elevate your hand above heart level to help get the swelling down. If you can't get an acceptable appointment with an orthopaedic doctor, go to your family doctor.