The insurance company is offering me a check, even though the accident happened very recently. Should I accept it?
Not without talking to an attorney first. Many of those settlement offers also include waivers, so if you accept it, you are essentially excusing them from any future financial responsibility. Remember that many insurance companies routinely offer low settlements. You could be getting a mere fraction of what you are entitled to. You owe it to yourself to have an attorney evaluate the offer before you accept it.