By all means you are describing a classic whiplash incident. Your neck will feel progressively tighter, warmer and stiffer as the day goes on, and will worsen over time if neglected. I recommend getting yourself immediately to a chiropractic physician for a complete evaluation. Do this without any further delay. The sooner you begin treatment, the sooner you can be out of pain and on your way to healing.
Doctors of chiropractic are physicians skilled specifically in dealing with this type of injury, they do it every day, and their experience is to your benefit. By choice, they prescribe no drugs and do no surgery; their painless manipulative skills are generally second to none and are recognized by the medical community as being most effective in just this type of case and low back pain. If you don’t have one already, ask around among your friends to find out whom they trust. During your examination, the doctor may detect things for which he may refer you to another type of physician, such as a neurologist. Though you may certainly use Advil or whatever to reduce inflammation also, beware of any advice to rely solely on drugs or heating pads, as these band-aids do not address the root cause of the symptoms and may make the condition worse.
The damage to the delicate posterior joints of the neck is done by the hyperflexion/hyperextension of the neck during the incident itself AND by the subsequent inflammation of the torn joint capsule fibers and ligaments. The more time goes by, the more inflammation is allowed to progress, and the more fibrotic scar tissue will develop in the area, setting the stage for (a) microadhesions of the contractile scar fibers to nearby nerve fibers, tugging on them and causing chronic pain indefinitely and (b) susceptibility to re-injury at substantially lower forces than would have normally been the case. Expect to see on x-ray some loss of the normal lordotic (forward) curvature of the cervical spine. This is usually permanent, unfortunately. However, with the doctor’s manipulations and other treatment modalities, any pain and joint dysfunction can be kept to a minimum, giving you the optimal chance at recovery.
Above all, do not discuss this occurrence with any insurance company employees until you have had a chance to discuss it with your own legal counsel to protect your rights. But first and foremost is your health, so get to a chiropractor pronto. I’ve had a several of these rear-end collisions myself, and they are no fun. Without my chiro I would be unable to work or function in daily life. Follow the treatment plan faithfully, and you will be glad.
P.S. ICE ONLY, no heat, for at least 48 hours!! And then only MOIST HEAT if you use heat. No heating pads, please. Begin a daily journal in which you record what happened and details of how you feel each day. This will help your team of professionals to help you. Best wishes for a speedy recovery.