separation anxiety?

Hannah • This is my first child and my husband, Mishon and I are so excited!
Can babies have separation anxiety? I feed my 4 month old before I left the house and I was only gone for 20 minutes and I get back and she is crying/screaming bloody murder. No joke, the second I pick her up, kissed her, and talked to her she immediately calmed down. 
I feel like a horrible person. I feel like every time she cries now, it's my fault. I don't know, I just feel horrible. 
Advice or suggestions.