Hello and welcome to Ask A Doctor. I have read your query and here is my advice.
He may have nasal allergies. Nose bleeds can be caused by allergy. Other signs of allergy include a personal or family history of hay fever, asthma, and eczema.
Does your son also have cough, a fast respiratory rate, or his neck muscles pulling when taking a breath? These can be indications that he is working hard to breathe and are seen in respiratory infections below the nose, for example: croup ,pneumonia.
It would be helpful to know whether the spots on his bottom are raised, flat, circular, irregularly shaped, or itchy.
Keeping your son well hydrated will make his nasal secretions thin and watery and easier for him to blow out. Putting a small amount of Vaseline inside the front part of his nostrils may ease the irritation.
Oral medicines that can be taken at his age are: Loratadine(a non-sedating antihistamine for allergy) or pseudoephedrine(a decongestant).
Hope I have answered your query. If you have any further questions, I will be happy to help.
Arnold Zedd, MD, FAAP

Hello and welcome to ‘Ask A Doctor’ service.
I have reviewed your query and here is my advice.

Nose bleed that your son is having is most probably because of the damage of the blood vessels in the mucosa of the nose due to congestion. It may help applying some vaseline with a cotton tip inside his nose so the mucosa there will be moist and will heal faster. Also advise him to not put his fingers in the nose, if he does that. About the spots in his skin, I cannot say much unless you upload a photo so I can have a look and advise a treatment.

Hope I have answered your query. Let me know if I can assist you further.
Regards,     
Dr. Klarida Papaqako