Is it possible for a four month old breastfed baby have allergies?

Yes. Infants can have food allergies early on to many items you may have consumed in pregnancy. Airborn particles are more likely to produce irritant effects ( like smoke or fumes) than allergies. Washing the nasal menbranes in infants with saline will reduce some of their chronic congestion.If they have eczema &or chronic nasal drainage i often send kids for food allergy tests, >1/3 are +.