Carrier refuses to assist with unlocking my phone.

They're the only one which can.

If they offer unlocking but some requirement isn't being met, ask them or see below.

If they don't offer unlocking, sell it to one of their customers.

(219803)

Only the locking carrier can unlock the phone.

If you are not one of their current, paying customers; getting them to do so may indeed be problematic.

Nothing much you can do about it. If the carrier refuses to unlock it, it can't be unlocked.