Hi.

Wonder if someone could help me with a sticky situation.

I´m working on a project that involves socializing with really nice people and they´re great. However there is one person who is really clingy, probably because she is insecure. She keeps following me around, is always trying to get my attention and interrupts me when I´m talking to someone else. She´s always in my face.

I keep distance from her, as I´m trying to show her I don´t care for her company, but I don´t want to be rude. I really dislike clingy people.

Any thoughtful advice would be welcome.

Maybe you're right. Maybe she is insecure.
But, before you can answer the how, you must answer the why.
Do you know if she has any friends? And if you don't, then possibly she doesn't have a lot of friends, and you gave the time of day to her which felt special. I know you don't like clingy people, but keep in mind, everyone NEEDS a friend.
Just sit her down and, heart-to-heart, unselfishly, let her know to let up a bit, and if she doesn't, then put it nicely that you don't think that you two would be great friends, but that you enjoyed her presence.
Finding the nice way, is the hard part. I know you can do it(:

Usually those type of people tend to look up to others for acceptance and reassurance that they are cool or popular or whatever the case is. Just be honest with her or hint that you don't like to be followed around. Or give her some work to do!