There's always a certain element of risk in changing employers, especially if you've been where you are for awhile and have a lot of stability. Plus you'll probably lose some acquired benefits like additional annual vacation time if you're in the US. But if you're diligent in researching the companies you interview with, and you're pretty sure that you're capable of performing the duties of the new job, then I think it's worth the risk. It usually works out. There are exceptions where it ends up being the wrong move, but you can improve your chances by making wise choices along the path to a new offer instead of just jumping on whatever falls in your lap first. I get the fear, I had a lot of it myself. But changing jobs was the best move I've made in years! I ended up making more money, with fewer responsibilities, and a more prestigious position. You can probably do it too if you make it a goal and approach it methodically.

Best of luck to you! I really hope you're able to make some change to reduce the stress, even if those changes are just a change in arraignment with your current employer. Stress is the number one silent killer in modern society. It causes so many different health conditions that it's easy to overlook that the cause is stress. In my last job I developed insomnia, lost a bunch of weight, my memory went to shit, and my blood pressure was always high. All of those symptoms went away within a few weeks of getting my current job.