This is close to, but not quite, Carpal Tunnel. It has more to do with muscles than tendons. If left un-attended it can turn into something called Repetitive Stress Syndrome, which cause micro tears in muscle fibers. The most important thing is to stretch!! Take the advice of previous posters and stretch before during and after!! And try to shorten your knitting sessions if your wrists and thumb muscles are sore.
Some stretches you can do:
Place your fingers of one hand on the palm of the other and bend them back until you feel it in your forearm. Repeat 3-4 times on both hands.
Hold your hands like you are opening a jar and shake your hands vigorously (you are doing it right when your upper arms jiggle)
Like #1, but backwards; place your palm on the back of the other hand and push until you feel it in your forearm. 3-4 times per hand.
Roll you wrists in circles. (when i do this I sound like a Rice Kristpies commercial)
Whatever you do, do not ignore pain! It is your body’s way of letting you know that something is wrong. Pace yourself and take care of those hands!!
Sorry for the lecture, but my SO is Phyical Trainer/Health Coach so I get this all the time. He gave me these stretches just for this purpose so they should help.
Take care and Happy knitting!!