I agree, the first self-injection is scary. I opted to have my wife do my injections, and that solved the left/right side problem too.
A practise tip I have seen but never actually tried, is to use a piece of fruit held between your legs as the target -- something with a tough skin like an orange or banana. Then you can practise as much as you like without pain. If you inject with whiskey, you make a nice dessert too