This is a very common doubt that plagues writers, particularly if they're new at the art. The only way to really know whether the characters you're writing are Mary Sues or not is to develop a strong sense of objectivity. You need to learn to pretend you have other opinions, other viewpoints, that you don't know what you, as a writer, know. Place yourself in the eyes of the audience, that's the only way you're going to find out. Like, for example, pretend you despise "cuteness" or clinginess. Does your character still have redeeming factors? Does she have flaws the audience can identify with? (remember: a flaw is only a flaw if it actually hampers the character; arachnophobia is not a flaw if the character never encounters spiders or never actually gets hindered in any way when she encounters one).
Being detached and unemotional about your own writing is one of the hardest skills to acquire, but it's arguably the best when it comes to ensuring the quality of your work.
And if you ever become a respected author someday, do try to keep this sort of thing in mind. I can't tell you how many authors I've seen who become so full of themselves in their maturity that they don't even consider the possibility that they too can make mistakes and write painful Mary Sues.