No! NOT before discussing it with your Personal Injury attorney.
Face it – the insurance company’s attorney works for the insurance company, not for you. As such, he/she is evaluated on how many claims they can settle, and at the lowest possible cost. The more your claim costs, or the longer it takes to settle, means that the insurance adjuster is not doing the best possible job.
Plus, if you settle too early, that settlement may come before you know all of the current and future expenses resulting from your accident. Once you receive the settlement money, your claim is settled, and you cannot return asking for more if you need more medical treatment or a longer stay in rehabilitation.
Your Personal Injury attorney is the only one who can advise you objectively about the settlement offer, and whether it is best to accept it for make a counteroffer. That attorney works for you and in your best interests, so trust him to give his best guidance.