Responsibility of the insurance to guarantee car repairs after an accident

Good day!

I've had an accident a month ago and I took my car for repair and have signed a paper to proceed for repair under the advice of my insurance company.

After 1 month, I checked the status of my car and the repair shop asked me to transfer my car to another shop.

I drove my car for transfer I noticed that my car has some humming sounds, and it is shaking/having some vibration when it is accelerated to 60. I informed the shop and they said it will not be under insurance.

Now, what I am asking from my insurance company is to just make my car roadworthy and without the vibrations/humming sound but they are refusing as they are saying it was because of the normal wear and tear and not because of the accident.

But before the accident, my car didn't have any issues like what it has now.

My question is, do I have any right to ask the insurance to make my car roadworthy before it is released from the repair shop?

Thank you