What really helped me improve my typing speed is...Gaming. Would you like to try to simultaneously try to have 3 different conversations while something is trying to kill you, all of which you control with different keys? That forced me to type faster in a fun way.
Tying long papers for english class was also a good motivator.

When my fingers hurt after too much time on the keyboard, I...make sure I am using a wrist pad to support my hands on the keyboard, and that I am not getting angry and typing to hard.
A good stretch and taking a break helps too. Playing with putty can help get the kinks out of your hand by making you use different muscles in your hand.

My tip to improve your typing speed is to...Keep typing. There are many games out there to help. Put yourself in situations where you have to learn to type fast. Gaming really helped me.