In conversation with somebody today, I had this pithy thought: Jesus told us to repent of worrying, not anxiety. Worry is the activity of going over what might be if you don’t. Anxiety is the emotional state of being fearful about the future. Worry is a sin; anxiety is a condition. So we need to repent of worry and trust in Jesus, but that may not meant that the anxiety will disappear right away. Emotional states are too much subject to conditioning for that.
Instead, you can think of anxiety as being like the withdrawal effects of caffeine, or some stronger drug. People worry, because they are anxious, and the worry gives them minor relief from the anxiety. But in the long term worry feeds the anxiety. Attempt to stop worrying, and the anxiety hits stronger than ever. And the only way out is through. Repent of your worrying; stop feeding the anxiety. Trust Jesus, and understand that, if you obey him about the worrying, the anxiety will eventually go away.
Of course, you may always have an anxious disposition. Rejoice! Some people are unnaturally blithe, and never have the benefit of anxiety to remind them to turn to Jesus. Those people expect good things to happen to them, not because they trust Jesus, but because they tend to think the universe is bent to be their own personal servant. Each of us must tend the garden that he’s given.