Thanks for your question.
It sounds like you have correctly identified this as an anxiety attack, and while those can be very crippling, it is good that you have been able to rule out any health problems. It is great that you are aware of your body, breathing, and heart rate. By continuing to work on slowing down the breathing and the heart rate, it will allow you to also slow down the mind and make it easier to avoid getting caught up in these irrational thoughts. One of the most effective ways to treat anxiety is through breathing techniques, and if you are not familiar with any of these I would be happy to help you out with that. The difficult thing is that once anxiety gets past a certain point it can actually feel like you are having a heart attack, and that is a very scary feeling that takes some practice to gain control over.
If your anxiety is to the point where is preventing you from living a normal life, it is generally time to consider medications and you are taking the correct steps by meeting with a psychologist and a psychiatrist. Studies have shown that the combination of talk therapy and medication is most successful in treating these types of problems. In general, medication should only be used as long as necessary, and once you feel confident in your ability to manage your anxiety, you can start to transition off of it. In the short term, you may find that the medication makes this a lot more manageable and that you will be able to make more progress in counseling as well.
Although this can be scary and frustrating, it appears as if you are taking all of the proper steps to begin to get this under control, and I suspect as long as you continue that you will start to see some improvements. One of the best things you've done already is to be able to identify all of these things as symptoms of anxiety, and that already shows that you are already able to see things in the right perspective. If there is anything else I can do to help, please let me know.