Hello, I read carefully your query and understand your concern. Bloody sputum is also referred to as hemoptysis. Causes of bloody sputum include lung infection such pneumonia or bronchitis. I suggest to do a chest xray to confirm the diagnosis. Meanwhile,I suggest using anti inflammatory medications such as Acetaminophen to relieve the inflammation. I recommend to use a Mucolytic to treat the cough. I suggest to drink liquids and rest. To treat the nosebleed you should use a saline nasal spray . If the symptoms continue, I suggest using a cycle of antibiotics. Hope my answer was helpful. If you have further queries feel free to contact me again. Kind regards! Dr.Dorina Gurabardhi General &Family Physician