D.B.
Your mother is a damaged human being, for whatever reason. You can dig into that, or you can let it go. Either she is not aware that she only has pictures of one of you (which means she has some sort of mental illness or perhaps early-onset dementia of some kind), or she is super-angry at you and letting you know by excluding you from photos.
You can ask her about it, or you can have a sit-down, lay-it-on-the-line sort of conversation. Say that you are hurt by the exclusion from the photo wall, and you want to know why she does that. Then wait, and don't talk. But you have to be prepared for an angry answer, so be sure you want to go down that road.
I'd be curious about what your sister thinks and whether she has noticed, said anything, or complained to your mother about your exclusion. Is part of your resentment directed at your twin? Is your mother so damaged or so shallow that she can only love one person by shutting out another?
It would benefit you to get counseling. If money is an issue, call your town clerk and ask if there is a counseling/mental health office (some cities have them and they often take a sliding scale fee or something with a low co-payment with your insurance). You can also see if there is a pastoral care agency in your area - we have a group of clergy members who provide counseling to anyone (you don't have to be a member of one of their houses of worship), and they do fundraisers periodically to help underwrite the costs for those who can't afford counseling otherwise. If you can't find any agency on your own, call a couple of churches or synagogues and ask the minister/priest/rabbi offices if they know of any such agency.
I'd spend less time trying to figure out why your mother's relationship with her mother plays out into this, and more time about what you want to achieve with her and how much of that is possible.
Your mother is getting older and you are, understandably, facing the possibility of her not being around someday. But maybe you can't change her. Perhaps you should see her for lunch or dinner or a movie, but not in her home since it hurts you so much. And perhaps you should cultivate relationships with others - sounds like you have a good man, and maybe you can give to others (perhaps in a senior center or nursing home) and find an older person (or two or five) who give you perspective and warmth. It's okay to surround yourself at a holiday table with people you love and not necessarily people you are related to. Sometimes you have to create a "family" when life didn't give you a good one.