It's tough to say, but she's going to keep inviting you and circumvent your polite excuses by saying "Well which weekend DOES work for you?"
So the truth is going to have to be told. "Friend, I would love to spend time with you but I'm afraid it'll have to be a day trip. There seems to be something in that house that affects me, because whenever I've slept there, I've ended up with headaches, sinus trouble, sore throat (etc.) I suspect mold. I'm afraid I really can't sleep there or spend too much time at the house. Maybe it's a sensitivity of mine if it's not affecting you, but I'm wondering if you should have the house inspected. Hidden mold is a serious health hazard and you want to make sure you're not breathing it in either."
If you're not comfortable, leave off the part about the house inspection, but at least indicate that there's something in the house, you're not sure what, that's causing a reaction in you. It sounds as though you're not actually experiencing an allergy but a normal reaction to the dampness and filth, but if all you're trying to do is get out of sleeping over there, then blaming a personal sensitivity is probably the best way to avoid hurt feelings.