How long will it take for my anxiety to get better?

Making lasting changes is a very individual thing. Some people integrate changes more gradually than others. Give yourself a bit of time to work through it. 

Over the years I have worked with people with anxiety and panic attacks using hypnotherapy. Majority of people will achieve lasting results in three or four sessions. 

On the other hand, depending on the underlying issues we are dealing with, there have been those who have made a major shift after just one session. For others the change was gradual and ongoing, even months after the sessions were completed. Because everyone makes changes in their own time, I have found that it is best to evaluate the progress and to assess individual needs while we are working together. 

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There is no set period of time. It depends on what is causing your anxiety and how well you handle it. Anxiety could be specific, which has a specific cause, or generalised (‘generalised anxiety disorder), which has no specific cause. Both types usually involve fear. So the first step is to try to identify the fear that is causing your anxiety and work from there.

If you can identify the fear that is causing the anxiety and deal with that, relief may begin soon. Anxiety often involves fearing that you won’t be able to handle the fear when it arises. As you can see, one thing can build on another and make things worse. So developing skills to handle the fear is crucial.

If the anxiety is caused by being in a dangerous or abusive situation, the first thing you need to do is to develop whatever skills you need to remove yourself from the situation to one of safety.

Generalised anxiety disorder may take longer to treat than anxiety with a specific cause. It is usually deep seated and has become a sort of background to ordinary life, even when there is no need to be anxious and nothing to be afraid of. Learning to trust and willingness to practice skills will help.

Important in dealing with anxiety is self-observation and noticing how the anxiety feels to you. Learning techniques to reduce those feelings are key, such as learning to relax your body and learning breathing techniques. If you put in the time to do this when you are not feeling anxious, it will help you deal better with it when you do. In the end, how much time you are willing to work on yourself will determine the time it takes to find relief.

You might find that talking about the problem helps, however, what will work better is finding a resolution. If the problem is with a current situation, then either that needs to be resolved or your counselling needs to help you build your resources to deal with it. If the problem has historical causes, then again it will need to be resolved for you. So, how long your counselling takes is going to depend on what is causing the problem and the kind of help you are receiving in order to deal with the cause of the problem.

What I suggest you do is to go back to your counsellor and discuss your experience with them. Tell them that you felt better, but then felt bad again. They should be able to assist you to feel better, or at least help you make sense of what you are experiencing and give you an indication of the pathway they will take you down to resolve the concern. One session of counselling is not going to resolve the bad feeling. Sounds like you might need therapy. Ask your counsellor about that, too. Thing is, it takes time.

Hypnotherapy may be a faster solution, as Katherine suggested, so you might like to look into that, too.

Unfortunately there is no  definitive answer for your question or exact time frame. Everyone is different. Anxiety takes weeks, months and sometimes years, to build up to the point that it is unbearable. Once a person gets counselling, it takes weeks or months for the symptoms to settle down. If you do what your counsellor suggests, relaxation and meditation, then you should see a gradual improvement each week. This improvement us overall improvement. Most people have their ups and downs . Do not be discouraged by this. 

It is important to address the physical aspects of anxiety with deep breathing exercises and slow breathing to a count as well as progressive muscle relaxation exercises visualisation The thoughts of anxiety that lead to feeling the anxiety can be addressed by keeping a thought diary and allowing your thoughts to happen without them becoming overwhelming but treating them as clouds floating that come and go. 
CBT is a good way to address anxiety and can be done with a qualified therapist.
After your anxiety is more controlled you can address more deep rooted emotions that are causing anxiety to recognise that often events from the past trigger off anxiety in the present. For example if you experienced a parent as angry when you were a child it is possible that anger from a close partner or friend could cause you to get triggered into the same response you had as a child.
However as each person is an individual you need to find a therapist who is a match for you and will help you with your issues in the here and now so that the anxiety is no longer distressing for you.

Whatever the original cause, anxiety (or the fight/flight response) is caused by your primitive brain firing. There are various therapies that will "calm down" the firing such as CBT or hypnotherapy.

However, research has shown that it takes 90 days of practicing new thoughts and behaviours for the changes to endure. I recommend that you keep practicing your breathing every day for 90 days and continue talking therapy for at least 90 days to effect a real and lasting improvement.