No it's not controlling and manipulative, it's a reaction to cover for the deeper issue. I suffer with anxiety and I know that kind of inner conflict all too well. But at least for me, attempting to hide the problem will only hurt you, and eventually the relationship too.
And this is exactly why I think you need tell her. To let her know that this isnt an attempt to be controlling of her actions. I eventually opened up to my boyfriend about my anxiety and panic attacks [I'm F, late 20s] and he was able to see it wasn't petty jealousy or distrust of him that was driving my behavior. He used to be hurt and say 'How can you not trust me?'. Now hes the one who sits up with me at night talking when I have insomnia and holds me during panic attacks when I need it, and the more we talked things over the easier it is to trust and let go. I don't have to hide that side of myself anymore, I have a partner who can help me cope, like any other difficulty in our lives.
Please don't hide anxiety, people who love you want to help. Yes there are some people who can't or won't understand, but you deserve someone who wants to help you feel secure and at ease, and that you don't have to worry about things like Facebook etc. I had many relationships before that failed because I was too proud to admit something this, and also because they didn't appreciate or believe it was anxiety and not just 'being dramatic'. But the right person and the right friends will try to understand and help, and it builds stronger more trusting relationships in the long run.
Take care of yourself.