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This may be one of the side effects of Loratidine
because it dries the nasal mucosa making it friable and easily damaged during sneezing
causing bleeding. The blood shot eyes may be related to the allergy
she is having. If she has fever or increased bleeding there may be another cause like a Viral fever
which can also cause this picture. You may let her try steam inhalation which will hydrate the mucosa and prevent it from drying. Be careful while doing this and avoid keeping her face close to the steam. You may refer back to your Paediatrician if this does not subside.