You need to contact your doctor and let him know what is going on, you may need a change of meds or a different strength.
Sorry about this. I just realized that Cipralex and Lexapro are the same meds. I used to take Lexapro so I know exactly what your talking about. Yes, I do really think it's your meds causing the dizziness. I had it really bad when I was taking this med. I hated the dizzy rush feeling when I was drifting off to sleep. Do let your Dr know about what's going on though.
You should talk to your Dr about your symptoms. Dizziness is fairly common when you have anxiety but this really sounds like your medication. I've been on several meds myself and many of them have caused the symptoms your describing. It is kind of scary to be half asleep, turn over and get dizzy.