Recovering from a Bad Day

Thursdays are difficult for me. I feel very divided on them. You see on Thursdays I spend the entire day with Girl, and though she is so fun and sweet, she is also unbearably high maintenance. Lately she has decided she is terrified of being alone, so I can't move without her freaking out. Yesterday if I so much as stepped foot out of the room she screamed, "Mommy where are you? I'm alone and afraid."
Seriously, if she was in the family room and I went to the kitchen which is maybe ten feet away from her, separated by a wall with an archway (not even a door) she was screaming. When something like this happens, you can't do anything. Even going to the bathroom is impossible.
I don't know what to do with this new fear. My gut reaction is to just let her freak out and ignore her. I know she's fine, I'm still in the house, and I have to be able to leave the room so I can use the bathroom, take a shower, or even just make lunch. I need to have my sanity.
It is seriously worse than when she was a baby, because back then I could do things when she napped or by putting her in a bouncy chair. Now she wants to play or watch a show but have me there at the same time. It's almost more than I can take.
At the same time, this is the worst time of year for this kind of crap because with the single digit temps we can't go to the park. Also the library is closed for two weeks while they move everything into the new wing as they prepare for renovations on the old wing. So we're kind of just stuck in the house. Yesterday I was so close to losing my mind, we ended up wandering through thrift stores and Walmart for two hours just so we could get some time out of the house. Grrr Thursdays!