I don't know how old you are, but you do sound pretty young. That's not meant to be an insult, just kind of a disclaimer that this might just be a matter of living life and experiencing the things that grow you, getting over whatever insecurities that are natural in teens and early twenties. Also, having been married less than a year, you haven't settled into your groove or rhythm with your husband yet. Even if you lived together for most of the time that you dated, actually signing legal documents and saying I do can shed a whole new light on things. It can make you feel a different sense of insecurity and "what if?", because there is more at stake if it doesn't work out. You feel more vulnerable because you made a public proclamation that he is THE ONE. That could be a big difference in how you're feeling. You two are still trying to figure out the difference between being married and being single, how your lives are and must be for this new leg of your journey. And right when you're trying to pee on your turf and establish your place in his family of origin, there she is still lurking about. Hell, pee on her, too. The script has not been written. You write it. You are his family now. Don't be afraid to talk to him. Don't be afraid to ask for what you want, and give him what he wants. Don't be afraid to tell him--sharing, not whining--that you are feeling somewhat insecure, not exactly sure why, but would like some assurance from him that he is over her. Don't demand it. Present it to him like you two are a team, and your heart just needs a little maintenance to run at full capacity. Then, drop it. You can't get rid of her. Give him a chance to show you that he wants only you for a lifetime. The tricky part about that--it takes a lifetime to prove it. Enjoy the ride. Understand that it comes with periods of uncertainty, and just be prepared to love through those periods and learn whatever each moment has to teach you. Be open to that. That will build your confidence as a wife.
If you are uncomfortable being around this girl--especially until you feel solidified as a married couple--then don't spend time with her. Get it in your mind now that you can't control him. Don't try to stop him from seeing his mother or sister. Don't feel the need to tag along every time, to make sure that SHE stays at bay. DO spend time with his family enough to establish and build relationships. All you can do is tell him what you need from him and ask him to give it to you. You are, obviously, grown-up enough to be a wife. Don't bait your husband with statements designed to prompt him to comfort you. Come right out and tell him what you need.
One more thing: We all have ideas of what we think we'd do in certain situations. The truth is that we don't REALLY know until it happens. Fortunately for many of us, we don't have to find out. We get to live under the illusion that we've got it pretty much together. The flip side is that you also don't know how strong you can be until you get there. You probably thought that it would be no biggie if you guys were to ever run into this ex at the grocery store. Now, she actually has resurfaced, and you are trying to figure out how you feel about it and why and how to respond to it. That's very reasonable, and beautifully self-reflective. You're off to a good start by just asking yourself the question. If you just can't get her out of your head, maybe talk to a counselor who can give you tools for growing beyond that. Or just keep us in the loop; we'll guide you through it. Many of us are growing and have grown beyond this in our marriages and can relate.