How can I obtain proof of residence change?

If it's to prove that you live in the school district, most schools accept the following as documentation (which must be provided by your guardian):

Rental/lease agreement, mortgage document or current real property assessment document in the parent/guardian’s name; utility bill for water, electric, gas or telephone that indicates that the billing is in the parent/guardian’s name and is being sent to the house.

For the driver's license, this from the Washington DOT:

Residency:

If you are under 18 years old and your parent or guardian shows us proof of your identity and relationship, you may use his or her residential address as proof of residence. Your parent or guardian must live in Washington State and show us acceptable documents proving his or her identity and residence.

Proof of identity:

If you are under 18 years old, you may establish your identity with a Parental Authorization Affidavit. When you apply, your parent or legal guardian must:

Come with you to the licensing office.

Sign the affidavit.

Show us all of the following:

At least 1 document to prove his or her identity.

1 other document to prove he or she is your parent or legal guardian.

A local utility bill usually works or a monthly cell phone bill under yout name mailed to the new address.