Howdy Thomas,
Firstly, I approve of your first name. Good choice. Having a short leg is a relatively common thing. Several of my trainees have them. Something like 1/3rd of the population has a leg length discrepancy of between 0.5 and 1.5 cm. You are in good company. Just because you have a short leg does not mean that you cannot train. If your back is mildly pissed by all of this, get a belt and be conservative with loading. It will adjust and adapt as you lift. Now that you have a shim in your shoe, things should start feeling better. If you are near a Starting Strength Coach, seek them out and have them make sure you are lifting correctly. Eat, lift, and be merry.