Can using a medication that targets depression but is not approved for anxiety still wipe out anxiety?

I was wondering if perhaps the anxiety could be rooted in the depression and therefore getting rid of the depression could get rid of the anxiety. For me the drug I’m adding is Wellbutrin and I’m already taking Lexapro. I’m hoping this could better treat my social anxiety and also my depression.

wellbutrin gave me terrible anxiety.

Update & Lexapro side effects