I wouldn't worry about what anyone else thinks. If you're taking lessons, it's good to perform. For you own good. If you pay the same for lessons, you should be able to do the recital.
The thought that an adult is competing with the other students never would have entered my mind. I would just think it's great that anyone is taking lessons and is performing. If someone sees it as a competition, that's their business, but there are so many things that affect it, it's not an even field.
Just use a piece that's appropriate. I can see putting an adult in the middle of the group or toward the end just based on age. Most of the recitals I've seen are ordered by ability.
I have also seen adults do a duet with another adult, their child, or their teacher.
If you are the only adult who performs, you might encourage other adults to perform in the future.