The primary duty to avoid a collision is on the disfavored driver.
But the right of way is not absolute. The favored driver must also exercise reasonable care for their own safety. Fault may be divided between drivers if the facts support it, even though one driver clearly had the right of way. The driver with the right of way may sometimes be held to be partly at fault.
It is important to contact an attorney as early as possible. Waiting may make it more difficult to prove the insurance company is wrong if they try to blame you.