Lately I've been having quite bad anxiety/panic attacks. Everytime I have the slightest pain I start worrying a lot. I will get very dizzy and think I'm going to faint, and my pulse will start racing. I've had it up to about 140 bpm. I also feel like I'm choking and won't be able to breathe. I'm constantly thinking I'm going to die. Is this common?

Yep, it's very common.
You get a little twinge, you start worrying, your heart starts beating faster which makes you worry more and on and on and on.
I know this is easier said than done, but you just have to tell yourself that nothing bad is going to happen to you, if you don't "Feed" the attack, it usually passes quickly...at least it always did for me.
Another thing you should do, if you haven't already, is see a Doctor.

Yes, I have seen my doctor and then was sent to a psychiatrist. After talking with both of them I felt a lot better and stopped having my panic attacks. Lately they've been coming back and theyre a lot worse. Plus there are some symptoms I've never had before, so I've just been really concerned.

I know exactly what you are feeling. I posted a bit ago. The header is "Telling my story." You may want to read it and see if it helps!! I hope you feel better soon!!
Good Luck!!