Food allergies?

My new rescue has been having the squirts for about a week now. I had changed her food over before that but these have come on strong. After she was sick the first time she didn't eat for a day, then she did eat but she didn't have to poop. When she did it was solid and almost normal.

Today she ate before I went to work but didn't poop. I came home to a large (but solid) pile in her crate. When I took her outside it was more squirts. I brought her in and within five minutes she was sniffing around again, I took her out and she dropped a more solid pile that was still mostly wet.

I'm lost and confused here, could it be the food or what?