Firstly, good work on joining the gym. If you can afford it, get yourself a qualified personal trainer at least once a week. They will correct your technique, introduce you to other people in the gym, and act as a role model for social situations. Additionally, time in the gym with another person (trainer or friend) is positively associated with mental health benefits over time.
> The discomfort gets to the point where I blush
One of my most important learnings in new social situations was to not listen to my body. Blushing and sweating are physiological reactions. At the very worst, if you grind through it, your body will eventually give up and return to normal function after 15 minutes. With repeated exposure, your fight/flight mechanisms will temper down and learn the new normal. Having said that, sometimes I will take a 'smoke break' from social situations to go reduce my body temperature outside.
> My voice changes, my posture changes, everything changes.
My second most important learning is "be like dog". Dogs approach strangers and introduce themselves. They are interested in their new friend and listen to everything they have to say. If they could talk, they would be asking for more details, and complimenting their friend on their great choices. The key point here is that they are not waiting for permission to be themselves, sincerity is the default.
With respect to other commenters re: ecstasy, it is true that you may experience an entirely new mental / social state while under the influence. Making a friend for life in 30 minutes gives you some perspective on "normal speed" social interactions. Just make sure you remember that your mental state is altered: I attended raves for a year before I realised that I didn't like them, but the drug was making it impossible for me to have a bad time. There is also the chance that the drugs are cut with other substances, the risk of frying your brain, the risk of derailing into a junky. You should always have a non-negotiable end date after which you will stop using forever. And unlike what some other commenter said, MDMA != meth, never ever touch that stuff.
As a final comment, when I was younger I fell into the trap of reading Tucker Max, followed by 'The Game' by Neil Strauss, and then went down the rabbit hole into pickup artist forums. I strongly advise against this stuff. Pickup artist routines work (for social and romantic situations), but I found them deeply unsatisfying and nihilistic. These frameworks rely on impersonating a character rather than being yourself. There are useful tricks (in any social framework) for getting people to like you, but at the core you want people to like you for your true (and hopefully lovely) personality.