*tl;dr at bottom

So, I'll cut to the chase but here's a short background: I'm 19. My last relationship ended nearly 5 years ago when I moved to a different country, and I've had bad anxiety since, and shut off my flirting mechanism because I genuinely was not interested in anyone. I used to be smooth as shit, and still have occasional moments.

Present tense. I'm taking a gap year before going to college for my mental health. I've been going to the gym since November, and just recently saw this really cute girl about two weeks ago, and she comes every day. Now, I know that talking/hitting on in the gym is frowned upon, and I hate myself for thinking about it too, because I dislike speaking in the gym. But she's great, and seems like a nice person (by the way I've heard her talk/interact with her trainer and other people in the gym). I just need advice on how to approach her without having a panic attack. (I've already asked her if she was using x equipment twice and she said a simple no and I fucked off- but I could tell from her body language she wasn't repulsed by me, I even saw her check me out while I was deadlifting today.) I have started talking to almost everyone who comes to the gym now (about 4,5 people max- and it's never full blown convos, just a simple hey/how are you, so it doesn't feel like I'm just trying to talk to her and appear chill to everyone).

TL;DR: Has crippling anxiety and gets super nervous. Sees amazing girl in the gym, has no clue how to approach her. Went up to her twice only to chicken out and asked if she was using equipment and then just turned around and left

also side note, do people do handshakes when introducing themselves to girls now? I was a kid when my last relationship ended, I have no fucking clue.

Cheers guys, hope y'all have a good day.