Pregnant 4 months postpartum?

Hello! My baby girl will be 4 months old tomorrow, and I keep having the feeling that I’m pregnant. I haven’t had my period since having my daughter, and we were breastfeeding until one month ago. But I have felt really tired, lightheaded, dizzy, and nauseous. But my hair is also falling out so I’m wondering if it’s just my hormones changing. Is it possible that I’m pregnant even though I haven’t had a period? Or is it most likely something else? I will take a test when I get home... just curious if anyone else has been through this?