I've had this before a couple of times, each time to varying amounts. I think it's to do with it being so cold at the moment, your finger muscles aren't warmed up so they are vulnerable to damage. It'll be your middle finger cause theres a lot of stress on it from pulling up the bars all the time.
I would recomend, however annoying it is, not riding until the pain has gone and it should heal eventually.
It may be something to do with grips but i could never be sure with my pain; perhaps the grips are too fat which means the finger can't wrap around the bar enough and is struggling to hold it. Or it could be the other way and the grips are to thin meaning the hard surface of the bar isn't giving your finger enough cusion.
But yeah after having a similar sort of thing before i can only recomend to wait until the pain heals.