Anxiety is a normal part of life and we cannot exclude it completely from our lives. It becomes a problem when we are no longer able to manage it. Saying that there is a "cure" would seem to indicate that someone who had excessive anxiety managed to learn how to contain it, not that they had been "cured."
In fact, anxiety also serves a useful purpose and that is as a motivator, not the terrible destructive force that many people believe it to be. Therefore, it can be seen in both a good and a bad light. But removing it from your life completely is unrealistic and would be unhealthy. I believe your counselor is indicating they had excessive anxiety and have managed to learn how to contain it. Good for them.
No, medication is not the only way to handle excessive anxiety. Since you indicate that your's came suddenly only a month ago, I would think that there is something that has caused you to become concerned about something in your life. Considering that you are 20 years old, I would think this might be regarding your financial situation, education or personal relationships. All of these things need to be considered and explored. For everything there is a way to manage it, but the 1st step is to find out what it is.
In the meantime, in addition to your counseling sessions, I would think you need to look at lifestyle changes and the things that you need to incorporate in your life which may be lacking right now. The fact that you are not getting sufficient sleep at night would lead me to believe that you would be more anxious during the daytime. This is a natural reaction to insufficient sleep.
I'm not sure what your treatment plan is and what you and your counselor are working on, but you might want to take a look at our Tips column where we do have some things I think would be helpful. I would recommend that you watch the relaxation breathing video tutorial and I would also recommend that you look at these simple exercises which you can do. Please don't think that exercise is something that you just do for your physical well-being because research has proven it to be a very powerful way to help us with stress, anxiety and depression. When we exercise the muscles begin to promote the production of substances which help our mental outlook on everything. Therefore, it is not just to maintain your muscle strength, but your mental health as well.
I hope you have found this helpful.
Dr. Farrell