What really helped me improve my typing speed is...typing every day. I first learned to type through a 6-month typing course in high school a LONG time ago. In secretarial school several years later, I improved my speed, and when I became a secretary, typing became part of my everyday life at work.
Take a typing course to learn to type properly. I type so much that most of the letters on my keyboards (at home and at the office) are worn off, so I couldn't look at them even if I wanted to haha!
It takes time, time, and more time, but once you learn to type without looking at the keyboard, muscle memory takes over and you type without really thinking; your fingers type some words "automatically" and muscle memory helps you to increase your speed.
Good luck! Don't give up! You'll get there!