I know what you mean, by feeling like the unnecessary wheel. It sucks, frankly. If people want me around at this point in my life, I think I'll just let them come to me.
You shouldn't feel pressured or stressed about finding your significant other by a certain age or deadline. That's just ridiculous. Really, there is no right or wrong time for you to do what you want to do. Especially finding that right person. Personally, I feel as if my 20's are the years where I start to make something out of myself and chase my dreams and goals like crazy. So, a relationship is the furthest thing from my mind.
If you just want to meet new people, there are steps you can take to overcome your anxiety. You can try exercising more often if you don't already do so. Moderate exercise has been proven to help many patients with anxiety or stress related problems. Running in particular can remedy anxiety. Also, consider searching up some breathing exercises. Doing a few of those when you're starting to feel your anxiety creep up, can really help you out in a pinch.
You can easily meet new people by joining a club, a volunteer group, or just changing up some of your hang out spots. Really, it's up to you how you want to go about it.