I really do feel for you! Your 'friend' is using every trick in the book to make you feel insecure. I'm sure you can compete with her on the personality front, and maybe you're equally as pretty as her if not more, but as you've become painfully aware, you can't re-write history, so there's simply nothing you can do to match her with memories of beautiful times spent with your man. And doesn't the little cat just know it!
I must say, I like your attitude - you're clearly determined to put up a stiff fight for this guy. Keep it up! The next time the three of you are together, allow these two old pals to have their moment down memory lane. Don't try to be 'nice' by jollying them along or asking eager-beaver questions, but don't sulk or walk away either. Bear in mind that these hilarious reminiscences only really work when you've got an audience swooning with awe and envy. Don't be that audience!
So simply stand there with poise and dignity, sip your drink, and let them get the silly old memory over with. I'm sure your boyfriend will soon start to miss your involvement in the conversation, and if a guy has any sensitivity, he'll quickly try to change the topic so it includes you too.
But that's only a strategy for dealing with this irritating threesome - your work doesn't end there! Without drawing direct attention to your reservations about this woman, I urge you to reduce the time you spend in her company. Engineer evenings out with other friends - if you don't have anything in common with your new man, now would be the time to introduce him to your wider circle of buddies. Plan lots of fun time together - be an exciting, inventive girlfriend. This is YOUR chance to start building memories with this guy (ones that don't involve THAT woman).
You're right not to mention your insecurities to your boyfriend - the relationship is too new, and until something happens between your man and this woman (and maybe it never would), the issue is YOURS to deal with. But that's not to say you can't confront HER. Do you consider her a friend at all? If so, you can appeal to her as a member of the sisterhood. Simply put it to her that it appears to you that she has the hots for your boyfriend. I advise you to keep your confrontation that light and simple, and then to wait for her response.
She's sure to be stunned by such an upfront statement. Expect a denial. But then, if this woman is even half-decent, she'll almost certainly slink back into the shadows where - let's face it - she belongs.