Based on the facts you laid out it doesn't appear that you bear any fault for the incident. The other driver violated your right of way by negligently entering your lane resulting in the collision.
Typically rear-end-collisions are the fault of the rear ending car (you) in your fact pattern but your collision is the exception being that you were lawfully in your lane when another car "cut you off". There was nothing you could do to avoid the collision so you are not liable for the crash.
Yes and no. Not your fault that you were cut off etc, but generally, each driver is supposed to keep his vehicle under proper control and avoid hitting car(s) in front. Report it to your insurance company and they'll sort it out.
Simply report it to your insurance company to resolve. That's why we all have insurance. Good luck.
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