What happens when you have a panic attack?

I have anxiety but I am not sure if I have had an acually panic attack before. The first time I thought that I might have had one was when I was sitting in class and I was getting really annoyed by the people sitting next to me while I was trying to do my work and I started getting shaky, it was hard for me to breathe and I was trying not to cry but I was able to calm down. It was really weird because I had never freaked out so much over something so little. Another time was when I was meeting with my advisor and she kept getting in my face over a project that needed to be done and I got all shaky again had trouble breathing and had to leave because I couldnt stop crying and hyperventilating. A few months ago I was just in my house and my mom was on the treadmill. The noise of her on the treadmill doesnt usually ever bother me but I was so bothered by it I had to lock myself in the bathroom and curl up in a ball and I started crying and hyperventalating. So pretty much what happens to me when I freak out is I feel really floaty or shaky at first then I have trouble breathing and start crying/hyperventilating. I know panic attacks are supposed to be really scary for people but I have never felt like I was dying just like I was going crazy. What really happens when you have a panic attack?