It does feel really hard to figure out how to meet people when you don't have something like school or an activity you're participated in most your life!
Something you can do is get out and try new things. Check out your area's meetup.com. There can be a wide variety - and some oddly specific - groups that organize through meetup, so there's a good bet you might find something that interests you! If a group seems pretty big/diverse, you might find it easier to just show up to their next scheduled get together. I know one thing that helps me when I'm afraid to try something new with new people is getting to "scout" ahead of time. So, when going to a new place, I check it out a couple days ahead of time or give myself plenty of time to get there early, so I can find the place, find the entrance, etc. You might even be able to contact an organizer with questions (for example, it can help me to ask about the atmosphere a group has together or just to double check that an event is happening at x time in x place). Most meetup.com things I've seen are offered for free, so those could be an easy way for you to get out and meet some new people!
Facebook can also be a good way to find cheap/free local events! Browse the events for your area. You can find a wide variety of things to try doing this and can find some really interesting ones you might not have thought about trying on your own!
Another thing you can do is just go searching for new opportunities. Do you enjoy working out? Ever been curious about martial arts? Have a gym in your area that offers some interesting workout classes you'd be willing to try? Usually gyms offer a free class or a couple of free classes, so you could pick a class you want to try, go to it, and see what the atmosphere is like and if you want to keep trying it for a few more classes (or beyond)! Something like this can be less pressure because the focus isn't on socializing - it's on the workout. So, if you're finding the socializing awkward, it won't last too long because you'll be starting the next exercise soon and you can disappear after the class ends. (Though I find that lingering after a class, even just to listen to others who've been there longer and know each other well, is a great way to start making some relationships with people attending. People start remembering your face when you hang around and usually start trying to include you in conversations and such.)
How do you feel about art? Look up your local art studios, ceramic painting places, etc. Do they do any events or offer any classes? Pick one you're interested in and show up to that! Again, the pressure is off having to socialize, but you may also meet some fun people there. At the very least, you'll get out of the house and will have met new people, and that in itself can feel huge and important and even empowering.
Volunteering is also a great way to expand your horizons and get out there to meet new people! (It'll also look good on your resume if you volunteer for a good chunk of time, if building up your resume is something you're looking to do.) Any local food banks or soup kitchens looking for help? How about your local hospital? Local animal shelter? Maybe even the local zoo or aquarium has some volunteer or intern opportunities. Does your city's webpage list any volunteer opportunities?
Since you're LGBT+, are there any LGBT+ organizations in your area? Do they have regular meetings or volunteer opportunities? This would be a great way to meet people that you know are more knowledgeable and accepting of LGBT+ issues.
There's a lot of options out there to you that you probably don't even realize are available to you! Finding something you're excited about might help encourage you to get out and meet new people more often.
Since you have social anxiety, I know many of these may seem hard/daunting, but at least look into them and do some research about them. It helps me sometimes if I get myself informed and then give myself time to get used to the idea of trying whatever it is, then making a specific plan for a sort of deadline to set myself. It took me several weeks to join my current gym, but now I absolutely love it, the people are so accepting, and I'm completely comfortable going there. So, give yourself time and do what you can! Are you seeing a therapist or any other professional about your social anxiety? Do you have some methods in place that help you cope with and get through life with your social anxiety?