The most common piece of advice is to practice performing. And, it's important to treat it like practice; the type of practice where you don't just go through the motions, but where you problem solve as best as you can, and where you expect to have trial and error. You need to have an environment which allows you the freedom that you personally need to truly practice performing in a problem solving manner. You'll want to take note through unemotional observation of what didn't work, as well as what did work. For your sake and your sake alone, you will want to be capable of identifying what didn't work and then make a plan for next time, and don't apologize. Magnify the good for the sake of building upon it.
Fear is an experience of perception. Sometimes this experience is so intense it is like an opaque wall that blocks out everything else. Your goal is to start to see through it with a higher or wiser perception.
I know somebody who was deathly afraid of flying. Along with everything else, he hated landing because he said it always felt so bumpy and that could make him feel as though it were out of control. That perception created an experience of fear for him during these times. One day, he sat safely on the ground by an airport and watched plane after plane coming in for a landing. Each one of them landed perfectly safely. After several days of this and after having watched hundreds of planes land, he noted that every time, the plane looked completely steady and perfectly in control. The opposite of how he felt when he was sitting inside of the plane vs. being on the ground, watching them. From the ground, he observed the steadiness he saw in the planes, and imagined himself on the inside of the plane, experiencing the bumpiness and considered the fear this could bring. This observation made an impression on him and he realized that his fear was just perception, and false perception at that. As he flew in times after, when he would be sitting in the plane, coming in for a landing, and feeling the bumps, he imagined himself instead sitting on the ground near the airport, watching the plane steadily, perfectly, come in for a landing. And this would ease the fear.
I think there is something similar with performing. Both in the immediate circumstances, but overall and as you gain experience watching others and as you gain experience performing yourself. You can start to develop a perception that goes beyond the immediate circumstances, and you can start to see past the cloudiness of the experience of fear.
In birba's example of Horowitz, why do you think Horowitz kept playing? Why didn't he just get up and call it quits? Because he knew from experience it wouldn't last, so even though he may have been experiencing some discomfort, he could see through it in a way that made it so he could keep going. We have to find our own way of doing that.