I've been in a similar situation, not all your life details, but I was living overseas, along for Christmas. The guy I was sharing a house with went home to his family for Christmas and I was pretty much alone. I knew someone from where I came from in the US who said I could come over for Christmas. He was a preacher, but on Christmas day, I got a hold of him and he said he was just way too busy to do anything. They preach on Christmas day there, and he much have been genuinely overloaded between family and ministry.
But it got me really thinking and praying about having my own family. I'd been praying for a wife already. I upped the intensity and met my wife about a month and a half later.
Something that might help you is to keep in mind that you don't really have a right to go over to her house for Christmas. If she gives you that, fine. If not, it's not yours to require of her. If she doesn't invite you, that doesn't mean she doesn't love you.
She might have really good reasons for wanting to spend Christmas alone. Is she married? Maybe her husband doesn't want friends at home. He may want to relax, not have the rush to mop the floor and all the stuff you do when guests come. He may want to spend time with just their family. And she might not want to say, "my husband doesn't want you over" because that's throwing him under the bus and making him look like the bad guy, and he has legitimate reasons for wanting concentrated family time. Maybe they don't do that a lot. Maybe she feels that way. Maybe she thinks if she has a friend over, she won't focus as much on the children.
When you don't have anyone to spend Christmas with, Christmas is a lonely time. But when you have a family, it can be a super busy time. Sometimes, you may have more to do at work at the end of the year, not less, and you really need to work late. But if you do that, you have to stay up late to do the shopping and get Christmas cards. You are rushing here and there. Then if you have a friend who really wants to shop with you, that just makes things a lot more difficult. Your friend wants to talk. You have to arrange the logistics of meeting to go shopping instead of just rushing out to Walmart at midnight when you get the last Christmas card done. And you have to make those cookies for Aunt Sally, but if you do that, all the aunts and uncles need to have a batch of cookies for Christmas so you don't look like you are showing favoritism to Aunt Sally. Then there is this kids children's program, and you have to go to it twice. But first you have to buy food for the child's Christmas party. And you can't make the oldest kids middle school program because of the other child's program one night, so you have to go the other night. You don't get a lot of sleep, and you want a break from everyone for Christmas for that one or two days off. You can meet with your friend sometime and talk, but please, any day but Christmas.
That's a bit of fiction, but realistic fiction.
I think it's good to cultivate friendships with other folks who don't have families. If you have free reign of the kitchen, maybe you could find someone who needs a Christmas dinner and cook it for that person. If you live near a college campus, some international students get stuck with nothing to do. Stuck in the dorm when everyone is gone and the heat is turned down really low over the holidays. I've heard stories. Showing hospitality (love of strangers) is a righteous thing to do.
We had a single guy over for Thanksgiving before. I asked my wife if she wanted to invite him this year. She felt tired at the time and said she just wanted to have family so she wouldn't have to clean up as much first. I said okay. She's the cook and I don't want her worn out or stressed on top of all that cooking. Then he called to say 'hi', and she asked if it was okay to invite him. (It was my idea before, that anyway.) So I said yes, and so we invited him over for Thanksgiving dinner. We do like to invite people to things who don't have anywhere to go.
One year I was overseas and a lot of other people that went to church were young singles. I asked the pastor if there were any church events Christmas day. He just opened his home and guests came who didn't even go to church, expats who happened to be in town. We had a big lunch and it was a good thing. But it is a lot for busy people to open their home Christmas. And some people feel like they just can't do it on Christmas day because they are overwhelmed or want time alone with their families.