Dairy sensitivity?

Is it possible for my baby to be sensitive to dairy and not full blown allergic? I've read to switch to a dairy free formula when you notice blood in their stool or a rash. She has neither but has been very gassy lately and strains, her face red, like she's about to poo but doesn't. Her tummy is making a lot of noises when I feed her. She will wake up sometimes crying too. I am currently switching her to Similac Total Comfort hoping that'll help her! Anyone else experience similar symptoms with their baby and switched to a non dairy formula?