Test for covid.... my daughter's symptoms started with loud cough and then spread to rest is family before we discovered it was covid ( tested negative at first at pediatrician)

My kid with all sorts of seasonal allergies periodically has these symptoms. You might take her to an allergist if it persists for a month or more. Allergist might recommend allergy meds.

How dry is the air in your house? The bloody nose makes me think a humidifier in their room might help if you don't already have one. I get bloody noses and a dry irritated throat in the winter when the heat starts to run more--especially overnight--a humidifier helps a lot.

Did the cough start out of nowhere? When my kid gets a dry cough, it's usually because she was sick at some point, had a cough, and then it lingered after her virus cleared up (doctor says this happens when the throat gets irritated).

If it's out of nowhere, yes, I'd see a doctor.

If it's related to a prior virus, we usually do cough drops to soothe her throat and try to get her extra opportunities to rest her throat to help it heal. So less running around screaming with her friends at the park, more quiet activities at home with a lozenge and plenty of fluids, at least for a few days until the cough calms down.

I believe that there are water mist sprays for the nose, that could help with the nose bleeds. It might help with the cough if the air coming in through the nose is more moist? I don't really know, just guessing.

Maybe send a message to the doctor and see what they recommend.

Signs are bleeding nose, dry coughing with some mucus day and night. Should I take her to see doctor? Other than that, no fever and super active with no change in appetite. We already turn on the humidifier. Could she have allergy?