I would increase the Tylan 50 dosage to 1 ml twice a day. You can even give another 1/2 ml orally twice a day. Bloody mucus from the beak can be a sign of ILT, a viral disease. Usually there is bloody mucus slung all around the walls of the coop from shaking the head. It also can cause "pump handle respirations" as in the photo below. Avian inluenza, although rare can also cause blood in the sputum. The mucus is more likely in her airway or trachea. Chickens breathe through their air sacs, and although they have lungs, they usually get tracheal or sinus infections. Here is some reading about ILT, avian flu, and some of the other common respiratory diseases:
http://edis.ifas.ufl.edu/ps044
Infectious Laryngotracheitis
Synonyms: LT, ILT, trach, laryngo
Species affected: Chickens and pheasants are affected by LT. Chickens 14 weeks and older are more susceptible than young chickens. Most LT outbreaks occur in mature hens. In recent years, LT has also caused significant respiratory problems in broilers greater than 3 weeks of age, especially during the cooler seasons of the year. This is believed to be due to unwanted spread of LT vaccines between poultry flocks.
Clinical signs: The clinical sign usually first noticed is watery eyes. Affected birds remain quiet because breathing is difficult. Coughing, sneezing, and shaking of the head to dislodge exudate plugs in the windpipe follow. Birds extend their head and neck to facilitate breathing (commonly referred to as "pump handle respiration"). Inhalation produces a wheezing and gurgling sound. Blood-tinged exudates and serum clots are expelled from the trachea of affected birds. Many birds die from asphyxiation due to a blockage of the trachea when the tracheal plug is freed (see Table 1).
Transmission: LT is spread by the respiratory route. LT is also spread from flock to flock by contaminated clothing, shoes, tires, etc. Birds that recover should be considered carriers for life. LT may be harbored in speciality poultry such as exhibition birds and game fowl.
Treatment: Incinerate dead birds, administer antibiotics to control secondary infection, and vaccinate the flock. Mass vaccination by spray or drinking water method is not recommended for large commercial or caged flocks. Individual bird administration by the eye-drop route is suggested. Follow manufacturers instructions. In small poultry flocks, use a swab to remove plug from gasping birds, and vaccinate by eye-drop method.
Avian Influenza
Synonyms: AI, flu, influenza, fowl plague
Species affected: Avian influenza can occur in most, if not all, species of birds.
Clinical signs: Avian influenza is categorized as mild or highly pathogenic. The mild form produces listlessness, loss of appetite, respiratory distress, diarrhea, transient drops in egg production, and low mortality. The highly pathogenic form produces facial swelling, blue comb and wattles, and dehydration with respiratory distress. Dark red/white spots develop in the legs and combs of chickens. There can be blood-tinged discharge from the nostrils. Mortality can range from low to near 100 percent. Sudden exertion adds to the total mortality. Egg production and hatchability decreases. There can be an increase in production of soft-shelled and shell-less eggs (see Table 1).
Transmission: The avian influenza virus can remain viable for long periods of time at moderate temperatures and can live indefinitely in frozen material. As a result, the disease can be spread through improper disposal of infected carcasses and manure. Avian influenza can be spread by contaminated shoes, clothing, crates, and other equipment. Insects and rodents may mechanically carry the virus from infected to susceptible poultry.
Treatment: There is no effective treatment for avian influenza. With the mild form of the disease, good husbandry, proper nutrition, and broad spectrum antibiotics may reduce losses from secondary infections. Recovered flocks continue to shed the virus. Vaccines may only be used with special permit.