Any babies suffering from animal allergies yet?

Ever since we have moved in with my boyfriend's grandmothers our son has had sneezes, coughs, and watery nose and eyes. Only thing to change is having a dog around. She is already getting rid of the dog after some issues of the dog biting people including hurting the baby, she is done with the dog His pediatrician is pretty sure he is allergic to the dog. Is your baby showing signs of being allergic to animals yet?