How to store emergency contact phones related to a contact without creating new contacts?
I can see a few options:


create phone types (or perhaps even location types if it is more than a phone for an emergency) like 'parents phone'. This is what I have done myself for a youth choir
create a custom data set 'emergency phones' for individuals. If you set it to allow multiple records you can have a group with a label field and a number field
you could indeed use notes but I would not recommend that as it is unstructured data
an extension seems like overkill to me in this case