Pallas Good job on the playing and the recording. And, by the way, anything goes, when it comes to musician's stage attire.
As for playing in front of an audience... there are a few things to look at.
First - why are you there? Maybe to find out what others think. Or, to see if you're as good as you think you are. Maybe you've learned a piece, or pieces, well enough to show off a bit. Everyone likes to hear praise for their efforts; not so much to have our shortcomings pointed out, even if the critique might be helpful, a reality check. It's all good, as long as no physical harm comes to you, like a spotlight falling on your head, or tripping on your way to the stage. And, even those things, if you survive them, are a learning experience. Sometimes, we're paid to be there. And that's a different story.
Second - who are those people? Who's in the audience?
An audience made up of non-musicians is most common, and they are also the easiest to deal with (provided you're in the right place, playing what they want to hear). Non-musicians have no idea what you're doing. They either like it, or they don't. And they are influenced by things other than what you're playing - like how you're dressed, (Yuja Wang, Liberace, Elton John), or if you're engaging, whether you smile. I know, it's hard to not look nervous, if you are. But, the more you play in front of people, the easier it gets, maybe even to the point where you start to crave it.
An audience of musicians, or music students like yourself, is the most caring, most sympathetic, especially if they've been in your shoes (or pajamas). They feel your nervousness, but, if they're decent folks, they're rooting for you, like they would want you to root for them. Receiving praise, or critique from them, maybe getting pointers, or comparing notes (pun) is valuable information.
An audition is a very different story, whether it's for an agent, or a club owner, or a contest "battle of the bands" situation, and musicians should only put themselves in those situations if they are tough enough to survive a negative outcome.
I started playing music in public when I was 14, bass in a rock band, and gigged playing various instruments in various venues, into my early fifties. I've been fired, had amps literally blow up on stage, had the best and the worst gigs, the best and the worst audience experiences, could write a book. Oh, wait... I did write a book.
Anyway, you're doing fine. Keep at it. Have fun.