I completely agree with Zetti, if one councelor doesn't work out, it doesn't mean counceling in general won't help, there are a number of different techniques to help cope with these problems, and different councelors often use different techniques based on what they think will work for you. However, that doesn't always mean they will work for you. I have had some similar problems (mostly depression, but with tendencies towards anxiety) and I have gotten much better without ever going on any type of medication. I found that talking about stuff with a councelor helped to some degree, but what helped me the most was the techniques I was provided to help me cope, and break the cycles of negative thinking. In addition I have tried using other techniques I have read about (I study psychology) and found them effective as well. On the other hand I have a friend with very similar problems to mine, and she was prescribed anti depressants, which worked very well for her.
The studies for effective treatment on depression (don't remember when it comes to anxiety, but I believe they are the same) suggests that medication isn't always the best answer. That is not to say it doesn't work wonders for a lot of people, because they do, but they're not for everyone, and other approaches have proven to be more effective in many studies (again, depression, I don't remember about anxiety). If you don't want to go on medication, I don't think any GP or councelor would push them on you, and they certainly couldn't force them on you. Going to see your GP might still be a good idea though, I don't know how it works in other countries, but I assume it's the same as here, which is they can refer you to a councelor if you want to give that a try again. Also a lot of schools and universities have their own counceling programs, you might not even need a doctor's referral. If you feel like a treatment isn't working, let the councelor know, and you can work out alternative approaches. Also, remember that a lot of techniques take a long time. Some of the techniques I have used have seemed downright silly because they seemed "too simple" and almost like "why did I pay money for this, if it was that simple I would't have had this problem at all", but the truth is these things take time and effort. I'm not saying just anything will work, but speaking for myself, some of these techniques that I thought sounded too plain and simple have helped me greatly change the way I think, eliminating many problems.
Just remember that you're not alone, you'd be surprised at how many people struggle with problems like these. My point is, you never know who has these problems, because people get better all the time, and even if it doesn't seem like it, it can (and very probably will) get better! You've already done something good for yourself by seeking help once, that is a big step a lot of people are afraid to take, so even if it didn't work out the way you hoped, you have done the right thing, and if you just try again you really have nothing to lose, there's a great chance it will work out better the next time