I have totally been where you are at. One thing that might comfort you is that if you can ask the question "am I going crazy?" you are not crazy. "Crazy" people don't realize that what they are doing is crazy.
I thought I was going crazy before my diagnosis. I actually told my friends I thought I was going crazy and I remember them laughing and saying I seemed more "normal" than they were. You may have generalized anxiety disorder, maybe panic disorder, maybe OCD-maybe all three or maybe some other anxiety problem. The first key is to take care of yourself like the others said; decrease caffeine, do some vigorous exercise daily, eat well, rest when you need to. Don't let yourself get hungry. Breathe slowly and controlled deep into your stomach/diaphragm. This will all help with the physical symptoms. A psychologist (cognitive behaviour mod) can help guide you towards ways of coping with the mental stuff. Medication has really helped me (I take Celexa but it is being banned at my dose due to heart effects....the next few months should be interesting!).
Anyway, I was sitting in my university class of 60 soon to be health professionals and it came over me that I was going to stand up and yell "I am a fraud!" It was so difficult to stop myself that I left the class. This lead to panic attacks whenever I was in that room. With a university therapist I got the anxiety mostly under control. Ultimately though, it was the undiagnosed OCD that was the root cause. The incessant thoughts and images of violence, looking at a classmate and seeing their head cut off, images of knifing someone, phrases in my head like "kill, kill, kill". Total TORTURE! I felt like I had a constant conversation/debate going on in half my brain while the other half studied biology/physics/pharmacology. I was worried that I was a serial killer in disguise of a mild-mannered 20 year old student. I decided if I ever thought I was truly a danger to someone else, I would kill myself. Thankfully, I am still here (and the only things I kill are mosquitos and earwigs!).
People often get "obsessed" with things that distress you the most. Taking another's life is abhorrent to me. When OCD presented that thought to me, I got stuck on it-am I a danger? Am I going crazy? The thought reverberates around in your head which makes the brain pathway for that thought stronger so you have it more often. Then you just spiral downward and it's hard to see you way out. You feel guilty, depressed, worthless.
So like the others reading this post, most of us have been caught in that web. I have felt all the physical symptoms you describe. I have questioned my sanity. Thankfully I am on the other side now. Good intense therapy, a lot of writing and relaxing and mental imagery and medication has really made my life so much better and more fulfilled. It is not perfect; my therapist (who BTW I have not seen for 18 months as I am doing so well now) says there is an 80/20 rule. If you are "OK" 80% of the time, that is life-that is normal. Everyone has up to 20% of the time of weird stuff-unwanted thoughts, etc. She told me to think of the thoughts as an early warning signal-when I have them, I need to step back and re-evaluate what I am doing (do I need more rest, less coffee?) then get myself balanced again. I am now in my early 40s with two great kids and a loving husband and a great job. If I can make it, you can too.