Thanks for writing your query.
After reading your post, it seems that your daughter is having bronnchitis or bronchial asthma
Common cause of nose bleed in children can be due to injury by fingering in the nose. Near the opening of the nose, there is a collection of blood vessels, which bleed when injured.
You should get her investigated for :-
1. Complete Blood Count(CBC).
2. Absolute Eosinophil Count
3. Test for IgE.
4. Bleeding and Clotting time.
Also de-worm her with Albendazole
, if not done in last six months.
She should be given antihistaminic like cetrizine along with a bronchodilator
Any medicine should be given after getting her examined and after discuusing with her Paediatrician.
I hope this is helpful to you.