I would suggest two things (3 actually).
Stuck your fingertips in the hottest water you can stand. I am l;ed to believe the discomfort is caused by the blood vessels being constricted by the constant flattening by playing. The hot water opens them up again. Sorry Jaco, but the washing up would have helped!
Secondly (and I found this out) using flats makes the problem worse. I reckon this is because flats mean a greater surface area against your finger. That's logical whn you think about it, a bit like a grooved tyre and a racing slick.
To compensate for all these when I'm playing, I tend to lick my fingers regularly.