I have social anxiety in general, but my anxiety is directed more towards my health. I'm the type of person that will go to the doctor several times just for them to tell me there's nothing wrong every time and I'm not sure how to overcome that. As for my social anxiety, it's getting better. My therapist has helped me a great deal with that. I just can't get over my health anxiety.
I would have to agree with Paxiled. If your therapist doesn't specialize in treating anxiety, it's going to make it more complicated for them to give you the proper advice on handling panic attacks without using medication.
My question would be, what are you really anxious about? You said you have a hint of hypochondria, is your anxiety geared more towards illnesses?
Are you in therapy with someone who specializes in treating anxiety, such as a CBT program? Because if so they should be teaching you meditation and breathing techniques that may help you learn to overcome this. No guaranty it will work, but if you're not working on these practical steps your therapist isn't a specialist in treating anxious thinking.