In reply to mountain_noob:
I think this type of frostnip is relatively common, if a bit frightening the first time. The fact they are functional and normal colour (not swollen or going black) suggests it is on the mild side and will improve, although it does take time.
I had it in some of my fingers after skinning to the top of the Breithorn on a particularly cold (-28C) day earlier this winter. I was very worried I had caused permanent damage - numbness, no feeling or sensitivity to hot/cold and heavy peeling of the skin. Eventually, probably took around 6 weeks, things returned to normal - progress was gradual though and I distinctly remember thinking *some* of the feeling had come back but not all at one point. Climbing alpine routes later in the spring/summer I have not noticed any particular difference in sensitivity to the cold.
I think it is a waiting game, but if there is no signs of improvement after x weeks, I would let a doctor give you a second opinion.