Just do it, honestly. I have awful social anxiety with a heavy dose of imposter syndrome and yet I still go. I have done some incredibly embarrassing things in that gym as I got used to the equipment and the social etiquette but you know, I survived. And each time I went back I felt more confident. Start off with something simple that won't provoke anxiety and gradually work up. I didn't touch the free weights section for 4 months, I stuck to light cardio and some of the machines as I gained confidence and researched good form in my spare time. Sometimes my anxiety flared up and I left within minutes but it's ok because at least I turned up and then went back for the next session. You've got this!