Some ADs help with both depression and anxiety. At one time I used Lexapro and at a higher dose it did wonders for my anxiety as well as the depression I was dealing with. I have never used Celexa.
As mrsD mentioned, Buspar can be helpful for anxiety as well as Paxil.
Many doctors will say depression and anxiety go hand in hand. Not always true. I deal with anxiety/panic attacks but there is no sign of depression and hasn't been for several years.
I have not done well with ADs, many actually increase my anxiety. My Doctor and I stay with what works best for me with little to no side effects...Klonopin. I use it as needed, sometimes not using it for weeks at a time. Then there are times, like now, I use it more often and at a higher dose.
The challenge will be finding the right med(s) that help you...trial and error