Thank you for your query on Healthcare Magic.
The purplish color of the hand may be due to decrease in blood supply to the distal portion of the hand after the splint
due to a tightened splint because of swelling of hand.
Check for the radial pulse of the hand of child.
And call ER and consult the doctor there as early as possible to assess the blood supply to the hand.
Hope I have answered your query.