Dog Won’t Stop Barking?

I’m housesitting for two dogs. One is older and seems pretty mellow overall, however, the younger one seems to be suffering from severe separation anxiety. She’s been whining and barking at all hours of the day and night. For the first couple days I tried to comfort her and make her more comfortable with me. Sometimes she’ll cuddle up but still bark, other times she’s hostile. I’m four days in now and still have another four to go. I then looked up best ways to handle this and found most responses were to excercise and ignore the dog. The backyard here is big and when the two dogs would play it would work for a little while; however because of the heat the owners don’t want me to take them on walks, and now we’ve been having awful duststorms, which aren’t safe to be out in. So I’ve been trying to ignore her. However, this leads her to moving from barking at me from the door way, to the room, to right in front of me, until eventually jumping on the couch with me and barking in my face, along with nudging her head against mine (she seems to be a sort of pit bull mutt; and I’m 5’1 and admittedly not the strongest person, so it’s not easy for me to push her away something like that) Her bark is absolutely ear-splitting, and the house being rather large and empty cause her bark to project and echo. I’m at the dogs house, and have been letting both dogs sleep with me because I read that should help. However, she still whines and barks at me almost constantly, and now my allergies are pretty awful. That with sleep deprevation from being kept awake all night have really put me at my wits end. Any suggestions or advice is much appreciated!