Anti-depressants often have an effect on anxiety too, so this may be the first thing suggested to you.
However they do have side effects that might bother you.
I had issues with anxiety but was not depressed (properly assed by specialists so not just my opinion).
I didn't want to take an antidepressant, but tried, goodbye sleep and libido, didn't really work for heavy anxiety with physical symptoms/nervous going outside parts.
So a specialist gave me pregabalin (lyrica). It's approved for anxiety in europe, has other uses in other countries. He said that it didn't work for everyone, as with anything, worked absolute wonders for me.
Physical symptoms gone, was up and out, really a life saver. Side effects are sleeping a bit longer, bring it on I hadn't slept well in years and I love bed, not drowsy though if I didn't sleep lots. You absolutely cannot drink alcohol with it, it's collapse danger reaction so it's not an option unless you're willing to not touch alcohol. I don't drink so I was fine, but it's a serious no drinking one!
Other side effect that did interfere for me was that it's hard to memorise new material when studying, or keep things in head when reading. It's not a memory issue per se, I wasn't forgetful, I just couldn't recall and store things I read. This was a problem for me as I was studying, it was really a battle. I had no problems with things I had learned in the past, so still could do my fancy lots of thinking intellect work, but I couldn't get languages I was learning to stick in my head. In the end though I figured that if I couldn't go out the house or was freaking out constantly, life quality was interrupted enough that studying just needed to be put aside.
I took them for about two years, stopped recently, I fell like a genius because suddenly I can memorise and learn so quickly again, plus I'm flying through books! I don't regret at all though, they were a life saver for anxiety.