I have a very shy daughter. She plays well with one friend (who is a few years older) that she has seen A LOT. She plays well with 2 of her cousins that she is very close to. At all other playdates, she can be rude and not want to play with other kids. She gets very anxious in social situations. She does not like performing and does not like a lot of attention on her. If she's in gymnastics and people are watching and they clap for her, she gets very overwhelmed and can't deal with it. She is adopted from China and came home at 10 months.
We adopted again, and our son came home at 19 months. IMMEDIATELY we saw different social behaviors. Our daughter was (as a baby) swatting at people and not wanting to be close to others when we first brought her home. Our son waves and smiles at everyone all the time. Because they were so young when they were adopted, we have realized that this must be their temperament, most likely inborn. I can't change it.
So, I explain to people before they meet my daughter that she's shy (then they usually understand), and we privately work with her on how to behave around others. We tell her that we understand that she is uncomfortable, but that she does have to learn enough social skills to be polite in a social setting. At age 5, she is getting better with other kids, but playdates need to last more than 2 hours to give her time to warm up and have a good time. Also, when she's in the heat, all bets are off. She is very sensitive to the heat and cannot take heat and people at the same time.
I, too, was painfully shy as a child, but the rudeness is new to me. I would usually freeze when people talked to me. It was the weirdest thing--you know those dreams where you want to run away from the tiger and you can't make your legs move? I knew the answers to the questions the adults asked me and I couldn't make the words come out.
My daughter is not just silent and scared. She is outwardly rude when she gets uncomfortable, so I can't say "she's shy" and end it. We do need to work on it.
We know we can't change our daughter, but we do everything possible to try to get her to adapt to social situations enough to be a functioning adult. She is true introvert, and we do believe that is her inborn temperament. She likes to be only with her few very close friends or by herself. (Or with parents and grandparents, but grandparent comfort came with time.) Preschool friends and teachers, that she saw every day, soon became comfortable.
We have to work WITH her--pushing too hard only backfires.
If your daughter has not always been like this, then it could be a phase, and hopefully she'll pass it in time. My first thought was not an overattachment to you, but a introverted temperament. Introverts know people close to them well, and they feel comfortable with them.
Good luck!