I have had the same problem. Hang out with other friends,
quickly fill up your lunch table, when she asks to hang out with
you and your friends at break say, um sorry were doing something
important right now. If she calls you, don't answer. If she invites
you over, say no thanks. If she always asks to come over, say my
mom/dad wouldn't want any company over today. Taking it to the
extremes would be saying something like, "sorry my mom/dad hates
clingies."
Alternatively, why not find a quiet time and explain to her that
you need some time to yourself. If she is a friend, let's assume
that you don't want to lose the friendship. Ask for some times when
she won't bother you and agree when you will get together. This is
far less hurtful than deliberate avoidance.
Try to understand that a lot of people who are clingy lack
confidence. Getting the attention of a friend is a way of
confirming they are wanted and worthwhile. Try to make sure you let
them know you value their friendship even if you need time away
from them.