Yes. There is no such thing as "slight" symptoms of frostbite. You either have it or you don't. You may have pain from being cold but frostbite is when the tissue has frozen to death. It has to be surgically removed. If you have pain after being in the cold and it doesn't go away with heat, see a doctor as soon as you can.
Not if slight. Although this may help to clarify your diagnosis, there is not much that a physcian can do unless your start to develop problems with vasospastic disease or ongoing pain.