I would say one of the best things you can do is to consult a doctor or a nurse about broken necks. I'm a firm believer that education is a great way to get over your fears! That, and a doctor is a great person to reassure you that the human neck is stronger than portrayed in films. After all, they've probably seen broken necks, and, more importantly, have seen people survive and recover from broken necks!
Now, one thing that might help you is to think of the ways in which necks are broken and spines are damaged. It usually involves a great deal of force, like falling from a significant height and landing on your head. Even Dr. Google, who famously will tell you that you can die from just about anything, has a hard time coming up with results for, "Can you break your neck in your sleep?" At the amusement park, you might have to worry about minor whiplash if you go on a particularly fast rollercoaster, but if you could die just from having your head jostled, no one would live past middle school.
Exercise is one area where you could feasibly sustain a serious neck injury. If you're still taking a yoga class, talk to your instructor! You don't have to open up to them about all of your anxiety, but explain to them that you're worried about sustaining a neck injury. Ask if there are modifications to certain poses you can do that will lower your risk, if there is any. That's also something you could ask your doctor, since yoga is popular enough that they've probably seen yoga-related injuries before. Also, if you like yoga, but doing it makes you nervous, you could consider tai chi. It's gentle, but effective, and it's a wonderful way to fight stress.
Of course, the problem with irrational fears is that you know they're irrational! One thing that might help is to remind yourself of exactly how many nights you've slept in your life without breaking your neck. You say you're 26, so you've slept at least 9,490 nights. That's 9,490 times you didn't break your neck in your sleep. My dad and my sister are both really restless sleepers. They toss and turn all over the place. My dad does it so much he somehow manages to untuck the mattress sheet. He's 51 right now, so he's had 18,615 nights without breaking his neck. I don't know if looking at it that way helps you at all? I'm a hypochondriac, so I definitely understand that, "But I could be the exception," fear.
I manage my irrational fears, like I said at the beginning, by learning about them. I learn about what I'm terrified of. I learn the signs and symptoms and the countless, "Can you have x and not know it?" questions on *****! Answers. I learn the chances of it happening to me. Usually, the chances are miniscule. Less than half of 1%.
There's also exposure. For a brief period of time, I was absolutely horrified of choking to death. I had absolutely no idea how to manage that fear, and it overtook my life for almost a whole summer. I hardly ate, I was seriously depressed, and I was in such a high state of anxiety that I remember panicking and washing my hands for an hour after watering some plants because I was genuinely convinced I was going to pick up some sort of definitely-fatal virus from the hose. After a few days, when I exhibited absolutely no symptoms, I started working on trying to eat again. I started with very soft foods, and, if I couldn't eat those, I would swallow every bite with water. It was slow going, and I still sometimes have a hard time with things like baby carrots, but I was able to work through my fear. A few weeks later, I'd even gained back the weight I'd lost.
In your case, I would start very small. Just move your head a little bit. Nod or shake your head. Make tiny circles with your chin, or or roll your head back or forward. That's what your head is designed to do. Your neck has a joint, and, because of that joint, your head has been designed to move. Go as slow as you want, and make movements as small as you'd like. The goal is to gradually move up to larger, faster movements. However, because your neck is so stiff, it might hurt to begin with. That's also where education can help you: if you nod a little, and it hurts, your immediate reaction is probably going to be panic. But if you've had someone reassure you and explain to you that just nodding won't break your neck, you can try to use that knowledge to calm yourself down.
The thing I've found about being irrational is that, even if you know you're being irrational, sometimes having someone explain to you exactly why you're irrational is a huge help. Another example: not that long ago, I was absolutely convinced I had a certain disease. I'd done enough research on it to know that it was primarily in male smokers over the age of sixty, but I was absolutely convinced that I, a female nonsmoker under the age of thirty, had developed that disease and was definitely going to die. I went to a doctor, briefly explained to him my symptoms and what I was afraid of, and he told me point-blank that he had absolutely never heard of someone my age developing this disease. Logically, I'd already known that, but having someone else tell it to me gave it that much more authority.
That's about all I've really got for fear managing! I hope some of this helps you a little bit, at least. Good luck!