Am I Good Enough to Play for People?

For years now I have been playing almost every week with an Israeli pianist named Ra'anan (the name, not all that common, means "fresh").  We mainly play for our own enjoyment, working on songs for quite a while, playing them in different tempi and rhythms.  We have played at parties now and then, and prepared programs and played them at informal concerts.  But I know that we're not all that good, compared to professional musicians.  Last summer we played in a couple of restaurants, and they didn't ask us to come back.  We were too loud!
Through a friend of his wife's, Ra'anan got us invited to play at the Jerusalem Craft Fair, which has been going on for the past week or so.  The Craft Fair is a major event, drawing thousands of visitors, and there are four entertainment venues, including a major outdoor stage where the top singers perform.  Ra'anan and I were asked to play in the most inconspicuous of those venues, in an alley that goes between artists' studios, the only part of the Craft Fair that's permanent.
We located a drummer in our age range, a retired gentleman named Moshe who has gone back to music after a career in business, and we rehearsed intensely for a couple of weeks, meeting at Moshe's house during the few hours at noon when he knows that his neighbors won't mind hearing him pound on his drums.
The rehearsals weren't all that encouraging.  Ra'anan was very edgy and intense, and Moshe wasn't used to playing with us.  But after a couple of weeks we were at least listening to each other.  However, I recorded a couple of our sessions and didn't like what I heard.  My own playing was weak and mechanical.  There are so many excellent saxophone players around, why should anyone listen to me?
I became extremely nervous as the day of our performance approached.  Meanwhile, our gig was extended from two nights to three, which also didn't please me.  One night would have been fun, two nights became a kind of responsibility, but three nights turned the engagement into work!  Rather than being enthusiastic, I was apprehensive.
We had our debut last night, and it went so much better than I expected, that I'm amazed.
We prepared about 30 songs and figured out simple arrangements for them.  We mixed standards like "A Foggy Day in London Town" and "Dream a Little Dream of Me" with a few Israeli songs by Sasha Argov, Matti Caspi, and Yoni Rechter.  We played for about two-and a half hours, total, and people stopped to listen to us and even applauded.It often happens that I play better for an audience than I do by myself or in private, just with other musicians.  Once I'm up there on the bandstand with a horn, there's nowhere to hide, so I let myself go and play.