Welcome at HCM.
I have read complete details of your question.
I appreciate you for your work for such children.It looks that you are one of brave person.
Presence of severe pain
in neck can be due to muscle strain
,as there is no severe restriction of the range of movements of the neck so there does not looks to be a fracture but it will be best in your favor to have a x ray of cervical spine
The nose bleed can be there due to soft tissue injury
in nose .But nose bleed after injury is also a sign of head injury
.You should consult to a ENT surgeon first & rule out the internal injury to know.They are able to see the inner side of nose with help of a speculum.If there is no nose injury then cause for your problem should be in head.
Till then i will advice you to do rest avoid heavy strain.
Take a good analgesic like advil or aleeve.
Hope this all will help you.
With best wishes.