You need to get this mare ultrasounded ASAP, as I am CERTAIN she's in foal. I worked on a breeding farm for a number of years, and I've seen a lot of pregnant mares- and they ALL start to look like this as they get close to their time. Your comments about how she's "exploded" in the past month or so are a dead give away that the mare is pregnant- that's most likely why she was at the rescue you got her from in the first place, in fact. I'm thinking that this may have been one of those cases in which this mare was somehow bred by an undesirable stud, and whoever did this decided they didn't want the responsibility for the baby, so they shipped the mare off to the rescue place or tried to run her through a sale to get rid of her as quickly as possible. You have no way of knowing her history, as you've said, or what she was bred with, so the only thing you can do is take care of her as well as you can and hope for the best.
Are you in Australia or some other part of the southern hemisphere, per chance? If so, then that makes it even MORE LIKELY that this mare is in foal, since you got her during the first part of your spring last year. Unfortunately, it ALSO means that she's going to be foaling in late July, which is the dead of your WINTER- NOT a good time for a foal to be born. ( If you were in the States, or in Canada, it wouldn't be so bad, because late July is our summer, and there's plenty of time for a foal born then to develop and grow up some before the first of the winter storms arrive.) I agree with the responder who said it's likely the mare is carrying a filly, because as a general rule, fillies take less time to mature and come to term than colts do- and as a result, the mare will probably foal a little earlier than she might have otherwise. From now on, you need to keep a close watch on the mare, and start making a habit of checking her udder every day for signs that it's swelling and the nipples are enlarging. She should start to show real signs of making a bag about a month or so before delivery, and as you get to a week or so before, the mare should start to produce some clear colostrum, the first milk the baby will get when it's born. Once this happens, over the course of the following days, the colostrum will gradually turn cloudy, and 36 to 24 hours before delivery, it will go completely WHITE and become sticky to the touch, like honey or corn syrup is. At that point, you may even see small, dried beads of it on or around the mare's udder and nipples- this is the phenomenon called " waxing" by horse people. Once the mare waxes, she is within a day or so of giving birth, and you need to have her in her foaling stall.
Good luck.