Yes. When taking anti-depressants/anxiety meds, it takes time for the medicine to get into your bloodstream to level you out. usually 2-4 weeks. Your body needs to adjust to the new medication and it can cause anxiety for the short term. If it gets unbearable, call your doctor. He may need to try you on a different medication.
I took celexa about two years ago for a little more than a month. It gave me insomnia for the first week. My psych at the time didn't warn me. It was horrible. No doubt if you get sleep deprivation, that will cause some anxiety. I took myself off of it because I really didn't feel much of a difference. Maybe it will do more for you. Good Luck!