This must be very worrisome for you and it is something you will definitely have to have checked by her doctor. It could indeed be allergies involving the
noseNose fracture and sinuses. These allergic
reactionsAllergic reactions
Allergic reactions to medication
Dermatitis, reaction to tinea
Drug allergies
Febrile/cold agglutinins
Insect bite reaction - close-up
Intradermal allergy test reactions
Positive reaction to allergen
Transfusion reaction in the nose and sinuses can produce a lot of mucous and especially with infection, it is not uncommon to see some blood. But, these allergic reactions seldom begin right at birth. What is happening could indicate a lung problem, such as cystic fibrosis and, because that is a possibility, you should not delay having her seen by her doctor. If it turns out to be cystic fibrosis or a lung condition similar to it, remember that these are very treatable diseases and the sooner the proper treatment is begun, the sooner she will start to thrive.
Good luck