At first go !?!?
I've certainly have heard way way worse, even by more experienced musicians, and you have absolutely nothing to be ashamed of or embarassed of. Now 20-30 years down the line you will watch this again, and it'll make you cringe and then some, which means you have matured. Yes, agree with everyone else, that song is augmented and bettered with at least one more vocals, it's not a single lead vocal song. And yes, be nervous. It goes with it. I don't know anyone who hasn't been nervous at their first gig.You have strong and clear vocals, with almost no out of tune singing which is the most common thing present when being nervous. Very good one that one.
Mainly what I've found out, it is that you're exposed to "un-acoustical" sound levels, and light "levels" from the spotlight. Bright and strong. You feel "be-littled" in that environment. Open and totally exposed for scrutinizing, just as if you were butt naked. You just pluck the strings with to little effort and out comes this loud 120 db note that everyone in the audience hears like they would scrutinize you from top til toe with a magnifying glass. It turns out just as intimate!
No wonder one feels a little bit.. embarrassed. I sure did. Practice makes perfect. No matter how much you rehearse in your rehearsal space, nothing measures up to real gig experience. That's were the real practicing takes place. Get a second gig as soon as possible, and go compare your gut reactions towards the first one.
You have absolutely nothing to get embarrassed about. Keep up the good work!
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Can't help to pep your confidence and hybris, with this one, again. You would and should feel very proud, after watching this one:
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EDIT: If only my first gigs would've been as good as yours... way back in the early 80s.