After an accident, the insurance company for the driver who hit me says they will pay my medical bills and give me a " little something " for pain and suffering. They have asked me to sign a medical release. Should I take them up on their offer?

No, especially if you are still under the care of the physician.  Once you settle with the insurance company, that will be the end of your claim, even if your injury gets worse.  There may be other sources available to pay your medical bills while your claim is pending with the insurance company.  An experienced personal injury attorney will be able to help you understand your rights.  Most personal injury attorneys will meet with you for free to help you decide whether you need an attorney. 

By the way, you should never, ever sign the medical release that it sent to you by an insurance company.  While releases are sometimes important to the claim every release that we have ever seen from an insurance company is overbroad--contains no time limit--can be sent to anyone at all--and allows the insurance company to re-release the information to others.  There is no requirement that you sign their release and an experienced attorney can draft a release for you that protects your rights.