I burnt my finger and the best thing to do for it is ice it but I have raynaud's. What should I do?

Motrin or Advil (ibuprofen) A person with raynaud's phenomenon who burns a finger is ok to skip the ice pack, just take some anti-inflammatory pain relievers such as Motrin or advil, (ibuprofen) and then contact the doctor to see what care might be needed for the burn.
Don't ice now. Icing a burn is indicated only for the first hour or so after the burn. Beyond the initial treatment just use appropriate ointment or just keep the burn covered and let the body heal it. Continue to protect your hands from exposure to cold by wearing warm gloves when going into cold weather.