When I use the turn signal, the high beams come on.
The symptoms described lead me to believe that your Cadillac may be experiencing a failing combination switch. The Cadillac’s turn signal switch controls a variety of lights, as well as your cruise control, and receives more use than any other switch on your Cadillac. This may be why you are experiencing your high beams illuminate when you use your turn signal. To be 100% certain however, it may be time to enlist the assistance of a certified mechanic to come by and inspect your CTS with you. They will have the experience and tools needed to identify the cause of your Cadillac’s symptoms and make the necessary repairs, such as replacing the combination switch, so your brights only come on when you actually need them.