hello and welcome to HCM,
I do understand your concern regarding the blood coming from the nose and how worried you must be.
Firstly, you have nothing to worry about as blood coming from the nose if very common especially after an infection and especially in a child as their nostril
skin and mucous membrane
covering is very delicate and just a mild touch even with a cotton can initiate a bleed.
Your bleed would also have been because of the infection and vigorous blowing or cleaning of the nose.
You need to just take a mild nose drops like xylometazoline
drops for both of you and apply twice to thrice daily. Your doctor will know about this.
Do not attempt to clean the nose and do not blow the nose vigorously.
Watch out for spontaneous bleed if any and consult a doctor if that happens
take care and get well soon
Dr Sriram Nathan