I felt bad for you, Navindra, reading this. But, the "cramming the night before" should have been a clue as to what was going to happen.
I started saxophone at age nine, worked at it, dug into theory, and played in bands through high school, thought I was pretty good. Sat in with a jazz group one night and didn't have a clue; really embarrassing. The piano player told me I needed to learn my scales and learn as many "standards" as I could. So, I did.
Years later, I played club date gigs in South Florida - no song list, no rehearsal, just show up at the gig and play what the band leader calls. By then, I was pretty good; played every week, two or three times a week.
The key is two-fold. Either know the material so well that you can play it without even thinking about it, or, know your instrument to the point where you can play whatever you want, or at least well enough to play over the structure of the song, if you're improvising, or the song itself. That's it.
No amount of stage fright coaching can substitute for confidence. And the confidence comes from knowing what you're going to play to the point that the performance is an exercise in showing off your chops. And the more you play the material you know for an audience, the easier it gets. Don't quit the piano. But, start building a "bag of tunes", maybe a dozen or so songs that you can get under your fingers to the point where you can play them anytime, anyplace, with confidence. Best of luck.