Your kitten is very likely teething, and therefore needs to chew on things to help sooth his aching gums. The baby teeth take about 8 weeks, give or take a week, to all come in. Then they will fall out and the adult teeth will come in, which are generally all in by about 5 or 6 months old. Like humans, it is uncomfortable for kittens when their teeth are erupting, and they need to chew things. Of course, your finger is not comfortable for you to have chewed on. Provide your kitten with plastic drinking straws to chew on. Keep some all over the house, and when the kitten starts to chew on your fingers, grab a straw to distract the kitten to it. Also, put a shoe box or other low box on the floor for the kitten to chew on. My kittens teethed on the side of a shoe box. They also had fun jumping in and out of it.
Additionally, your kitten is likely still needing some suckling since he is still an infant, and in nature, if he was still with his mother, would still be nursing. Even though by 9 weeks cats in the wild eat some solid food, they do still also nurse. Once again, get out those plastic straws for him to indulge his suckling/chewing needs. There may be other things kittens would like to chew/suck on, but I only know about the straws and boxes.
The water squirting thing is overused, and over rated. I would never squirt an infant kitten for trying to fullfill his needs to suckle for comfort or chew to sooth aching gums due to teething. Even if it was due to rough play, which does not sound like the case, one needs to redirect cats to something they can do when one would like to stop them from doing what you don't want them to do. Just trying to make them stop doing something does not work, as they are doing it to fullfill some need and will keep trying to get that need, whatever it is, fullfilled.