Probably not under these facts. This is something for your insurance company to handle on your behalf.
However, there is a giant neon red sign glowing "DANGER" over the facts you present. If you have been reported to a debt collections agency over this matter you have serious problems going on with the claim. I would urge you to _immediately_ make an appointment to sit down with the adjustor in this case (not the local agent who sold you the policy) and find out exactly what is going on with their handling of the case. Bring all your documentation and your photographs and go through your side of the story until the adjustor really gets what is going on. This kind of thing should not be happening to you if your insurance coverage was paid and in force on the date of loss.
There are really two major benefits to insurance coverage, 1) indemnity and 2) defense. Indemnity means that the insurance company will pay on your behalf any judgment or settlement up to the limits of the liability policy you purchased. Defense means that the insurance company is obligated to provide you with a lawyer at no additional charge (since you have already paid for the lawyer by paying your premiums) to defend you from the allegations made by the other side.
If you are not 100% satisfied and you did not get all your questions answered by the adjustor, you may need to make a written demand for a defense. You may also need to retain your own attorney to represent your interests (both with the claimant's company and potentially with your own insurance company). I cannot stress enough the fact that you need to make sure that your own insurance company is on the ball and is working to protect your interests in this matter.
Many attorneys will offer a free or low-cost initial consultation. This does not appear to be any longer something which you can handle yourself. The original problem has now apparently gotten out of control and you are going to need professional help. You need to at least get an initial consultation with an attorney well-versed in insurance coverage and/or insurance defense issues. Even an initial consultation might give you a better idea of what you are facing.
I agree that you need to speak with your insurance company about this. You should also refer the collections company and the other insurance company to the adjuster handling this for your insurance company.
Your insurance rates should not have been affected if you were not at fault, so speak to your agent about that and, if that has happened, you should consult with an attorney.
DISCLAIMER: This answer is provided for general purposes only, and is not intended as legal advice made in an attorney and client relationship and there is no attorney and client relationship between the person asking the question and this answering attorney. The answer provided is based on the information provided, and the answer could change if the facts differ in any way from those stated in the answer. For a definitive answer you should seek legal advice from an attorney who (1) is licensed to practice in the state which has jurisdiction; (2) has experience in the area of law you are asking about, and (3) you have retained as your attorney for representation or consultation.