Sometimes after I roll and someone tries to go for a can opener while in my guard, or if I am sparring and my neck snaps back from a head shot I get a tingling sensation in my fingers.
I guess this is what a pinched nerve is.
It goes away after awhile, but how serious is this and are there any long term effects?
That happens to me sometimes also. It should go away after a while. If it keeps happening with increasing severity, see a doctor. You may want to see a doctor anyway.
In wrestling, they call it a stinger. It happens when the nerve in your spine gets pinched, so you lose some of the sensation in the corresponding limb.
If it keeps happening, it could result in loss of sensation and/or mobility in the limb.