Do you have an attorney who is representing you? If so, let them know how you are feeling. They may be able to help reassure you and tell you more about it. If you don't have an attorney, then it may actually be a good idea to ask for a postponement of the hearing and obtain one. By law, they are not paid by you, but would be paid a percentage of any back payment directly by social security if and only if they win the case. Handling this kind of hearing on your own wouldn't help prove that you can't work right now.
If you do have an attorney, try to remember that it is their job to handle it all. They don't get paid unless you win, so they have their own personal motivation to see that this goes well.
Are you feeling anxious about any one part of the hearing, or just the whole process?
When I went through my hearing, it wasn't nearly as bad as I thought it would be. I was terrified to go, but at the end, I left thinking, "that was it?" For my hearing, it was before a judge, as they all are, but it was not in a huge courtroom or anything like it. It was in a glorified meeting room that was pretty small. No one was there but me, the judge and my attorney. The judge did ask me questions, and I answered as honestly as I could about my symptoms and history. It was very hard to do, but not because of the judge or anyone else in the room. It was hard because I hate admitting anything is wrong...
It wasn't like being grilled on the witness stand like people see on TV. It was more like a conversation or a job interview - except that instead of talking about my skills, we were all talking about what I struggle with. The judge was not harsh. The judges talk to people with disabilities of varying degrees all day long, day in and day out. There isn't likely anything that you could say that would shock them or throw them off. Be humble, be honest, and it will hopefully work out ok.
It is awful to feel this bad, but there is one good side to it. It could help demonstrate very well why they should award you disability. Worst case scenario, if you end up feeling symptomatic while at the hearing, your attorney can use it to help prove your case. Remember, they have already read medical records about you, so it's unlikely to surprise them.
In the meantime, maybe holding some ice would help? Or something cold in one hand, and a warm cup of tea (or whatever) in another hand. I know this sound silly, but it is a well known way in some PTSD intensive treatment programs to ground out of a high panic state. No idea why it works, but it sometimes does.