I feel like keeping my relationship secret.
Why are you keeping it a secret?
I don't want it all over instagram.
It is okay to not tell everybody the news about dating but keeping it a secret makes the relationship seem wrong. Like your doing something that you shouldn't and it can harm the relationship.
I don't care as long as my girlfriend is happy.
I would talk with her and see if she is ok with it first. She might get the wrong idea like you are trying to hide her existence. But it is also good to keep things private in this over connected world.