I'm not an expert on suspension but...
First of all, I have to know if you changed both your springs and shocks when you decided to lower your car. It is NOT normal for your control arm to rub after lowering a car because the engineers involved in designing the shocks and/or springs take all the suspension components into consideration prior to designing the spring or shock (I should know, I'm a engineering student

) From the sounds of it, if you had installed new shocks and left your stock springs, then you can assume that your springs were really bad from the start and the excessive force on your new springs is too much to handle so it is giving way by rubbing. On the other hand, if you changed your springs and not the shocks, then your shocks are shot which is causing the rubbing because of the force exerted on the strings during turns and bumps in the road.
If you lowered your car properly and changed both your shocks and springs at the same time and your car is still rubbing, I can only make the assumption that one of the components you installed in faulty or the installation was done incorrect (ie: Left spring/shock was installed on the right side of car or vice versa).
I'm not an expert in any way when it comes to vehicle suspension, so don't take my word for it. Usually you should be able to lower your car as low as the spring/shock settings will allow and not have any major complications other than tire rubbing (if your offset to too low) but I've never heard of a upper control arm rubbing after a car being lowered so I would strongly suggest you get it checked by a certified mechanic since it's very unsafe to be driving right now. Good luck...
SaGe69