I smatched my finger and I'm worried thay it was sprained. ..My nail is bleeding and turning dark purple and its a but swollen, I am able to move it?

Trephination. Bleeding under the nailbed can be very painful because it can create a large pressure. In the er or an urgent care ctr, docs will perform a trephination (create a small hole in the nail to let the blood out) thus relieving the pressure and relieving the pain.
Have it evaluated. Try to avoid moving it too much for now. You may need a x-ray taken to see if you have a bony injury. Have it evaluated and get the appropriate treatment.
Let explain. Most likely when smashed you sprain your finger but what degree? The color under the nail it is from bleeding under the nail it is a good idea to have an x-ray to if the bone broken? Good luck. Thanks.