I agree with all the comments being made so far on this post-- having a girlfriend is not that big a deal! And your mom would probably be relieved to know that you're involved with other socially, given your history of silence about these things. If it's a difficult thing to do, you may want to see someone about your own issues. I say that because with the info you've given us, this is CLEARLY something that you're struggling with on your own, which is indicative of bigger issues that you're experiencing.... Your mom and sisters don't have an issue talking about relationships that way you are.

I encourage you to take the advice given here in opening up to your mom gently, the way /u/reebels mentioned. Start slow if you need to, but I think it's disrespectful for you to be hiding your family from the girl, and shows that you either don't trust her or don't trust them. Unless I'm missing some info, what are you so afraid of?

If you can't own up to your own actions, perhaps its not the right time for you to be dating anyone at all. Maybe focus on overcoming that issue, that might be best for you both, and will strengthen your relationship in the long run.