I agree with Les - start out playing simple stuff in front of folks, learn to relax, then get crazier as you see fit - you will soon find no-one notices or cares about the odd mistake you make.
As for recording, try recording yourself with a mobile phone if you don't have a PC/Mac-based recording system. Just get used to hearing yourself, and get used to playing live with others which just happens to be recorded.
I only ever jammed with friends for years and years, until I then got involved with some "jam sessions" with co-workers at work, after-hours. These jam sessions had gone on for years in the past, then went on hiatus, and when restarted I got dragged into it. I soon realized I was better than some other players, not as good as others, and everyone was OK with that, including the audience, which was often non-playing co-workers who just wanted to listen or support their friends.
About five years ago I played my first true public performance, at a charity fund raiser at a church, accompanying what is now two of my band-mates - mostly true accompaniment, but I also sang and played a song (cover). It went OK, and soon we were playing small cafes and pubs for free or fundraisers or similar. I started to notice that folks just wanted good songs/tunes, weren't all that hung up on technical prowess, although the odd time I did play a tasteful solo they seemed to appreciate it. Eventually we started to book paying gigs (one band mate has been gigging professionally part-time for decades, she figured we were good enough to start asking). Our main paying gigs are smaller pubs still, playing to a few dozen folks maybe, but we also play festivals where the audience can be in the hundreds.
And we record - did a CD last year, doing another later this year. We usually keep the first or second take, so obviously we all feel comfortable playing to the tape (well, DAW). While playing those basement/garage/cottage jam sessions with my buddies, I had experimented with multi-track recording, mixing, and burning to CD our rambling stuff, and I learned a lot from that, and got used being always recorded, I guess.
Word! If my wife walks into the room, I stop playing and pretend to be fiddling with the things. If one of the dogs walk in, I stop and find a treat that I can toss them to get out of the room.
Since my wife and I are in a band together (she joined the band a couple of years ago), if she walks in the room and I'm already playing, she'll play along - that is a really nice treat, being comfortable with each other.