If you can play it fine at home, I'd say it's more a psychological barrier than a physical one. The most effective way I've heard of to overcome this is through mindfulness. It's been studied in pro sports a fair bit, but if you practice maintaining focus on the somatic sensations of playing at home, that should be translatable to performing. Then, when you perform, the headspace isn't much different from practicing. I can find you the study if you like.
Another practical tip, record yourself at home. Puts a little pressure on, especially if you tell yourself you're gonna publish the recording online if it's good.