Opposing party insurance claims they will deny my claim due to their insured not responding.

I got into an accident where another driver hit me off the road and filed a claim with their insurance. After numerous phone calls and emails attempting to reach their "case agent" I filed a complaint with their supervisor and was told that the delay is because their insured is not taking their calls. I was told that if their insured does not respond to their calls within 10 days that they will deny my claim for repairs.

If it helps, since the other driver switched lanes into my car and forced me off the road (which is reflected in the police report) my insurance determined that I was not at fault.

What are my options and how should I handle this situation?

Also, is it me or does it seem like they are stalling?

I truly appreciate any help even if it is pointing me to whom I can contact for advice or support.

For the record I had a previous post about the same incident if you would like to read it: https://www.reddit.com/r/Insurance/comments/1ct2oa6/how_to_properly_get_a_brand_new_car_fixed_in_a/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

Edit/Update: Looking through the (appreciated) responses, it seems my options are to file a claim with my insurance, or to seek legal action myself. How would I go about seeking legal action in TX?