Swelling in finger - turns black and blue

Hi

Hope someone can help.  My mother is 61 and from yesterday, one of her finger has swollen to black and blue up to the first joint.  There is a lump underneath the swelling and when she presses it, it will move and it hurts a bit.  The swelling subsides in the afternoon and it swells up in the morning when she wakes.  Is this serious?  I have told her to go to the doctors but being stubborn, she insist on waiting for a 'few' more days to see what happens.  I'm concerned that it could be a blood clot or something.  Your help and advice will be much appreciated.