I'm sorry you feel the need to drink, as others have pointed out, it's not going to help, so I'm not going to focus on that.

Women very rarely respond to openers that just focus on their physical attractiveness.

Practicing social skills means noticing her to begin with, paying attention to her existence. You are in a shared space and obviously both are pursuing healthy bodies through exercise at the gym. Don't be obvious that you're paying attention to her, but just try to notice and take note of details.

Does she bring a book and read it on the treadmill? If she listens to something on her phone instead, try to catch a peek of what it is: music? podcast? television? movies? Find something that you can talk about as an opener, something you also actually enjoy, don't force it.

Once you have noticed the details, you don't open with "you're pretty" you open with "Hey, I noticed you're reading X/listening to Y/watching Z and I was wondering your take on subtext/meaning/musical structure/how funny it is/etc." You need an opening that gives you a reason to talk to her other than being pretty.

Once again, don't go out of your way to spy on these things and get marked as a weird stalkery creepy, but when you have a chance, take a peek into what's going on in her life.

Hell, you can even talk shop about gym and the kind of exercises you both approach. "I noticed you do some weight training, I've been meaning to get into that, do you think you could show me the ropes. My name is Blite."

It all comes down to starting with treating her like a person not like a romantic object of beauty. I know you didn't intend to be off-putting, but that can be off-putting and make someone feel like all you see is the outward shell and aren't interested in the inner person.

The final thing is that this means if you never have an opening to work with... well, sadly, let it go. You can't win em all, and sometimes the "you always miss the shots you don't take" attitude hurts more than helps. Maybe you just never had enough of a peak at their inner life because they're a private person, or maybe you just genuinely don't have a lot in common with them. Whatever the reason, let it go and look for someone you can find a personable, humanizing opener with.

The bottom line is women are people and they generally want to be treated like a person first, which means talking to them and treating them the same way you would trying to make any friend of any gender. Because it has to start with enough mutual respect to see them as a friend first, find common ground, and then after a while of getting to know each other in the shared space (maybe a few weeks of talking to each other and getting to know one another in the gym) then ask her out on a date.

I really hope this helps. You're not hopeless, you just need to change up how you approach this kind of situation. You also need someone willing to help walk you through it instead of just focusing on the drinking. Then you won't need to drown your sorrows because you'll have an actual path forward and be learning and executing better social skills.