Coughing bad: Pertussis (aka croup) and pneumonia come to mind. Very dangerous.
Blood in ears: tubes dislodged? Don't know about that but without fever, I'm not suspecting an infection. Maybe eardrum broke?
When my daughter had mild pneumonia, my doctor had me lay her over my knees twice a day (morning, night) and cup my hands and kind of hit her back to help dislodge thick mucus. Everyday. We used cold water vaporizers really close to her for the same reason. Lots of warm soups, teas, water. You may be giving her an expectorant type med without the required water amount. (I don't know how young you give those things to kids)
She having ear pain? Try Tylenol and heating pad on ear.
My mom used to sit me in the bathroom with the hot shower running.
I think your regular doctor should be able to tell but insist on getting in today. If not, consider one of those children's clinics that accept same day appointments for emergencies.