There can be several reasons of your symptoms, although without being able to examine you I can not offer you the specific advice on diagnosis and treatment that you need, but I would try to provide you some relevant information about your health concern.
Most likely, your symptoms may be due to nerve irritation in the cervical (neck) spine because of injury/prolapse where contact between the edges of the vertebrae can cause neck pain. In few people, this pain may be referred and perceived as occurring in the back of head, shoulders, arms or chest, rather than just the neck. Other symptoms may include vertigo, nausea (dizziness) that you felt. Additionally, symptoms are like neck pain (electric like sensations) and stiffness can be intermittent. It will be best that you consult a neurologist who would like to prescribe Pain killers, steroid and muscle relaxants. Other treatments could be cervical orthosis such as a soft cervical collar/stiffer neck brace to restrict neck movement. In addition, cervical traction may also be suggested by the doctor, if condition is severe. Hope this helps.
Wait for the pictures of your neck before you go to a neurologist. Could be you wrenched something in there, and the docs will refer you to a specialist if any nerve, blood vessel, tendon and ligament, or muscle damage is serious. But anytime you're in a car wreck, the impact alone, plus any injury by the airbag, it's going to bruise you up, wrench up muscles, and you're gonna hurt for a while. The Carisoprodol is to relax your muscles, so that's good. I don't know why tightening the BP cuff made your other arm hurt, don't know enough about circulation to comment, but obviously when you get your X-ray results back and talk to your doc, he can explain it for you.
While you wait for the results, you can put heat to your arm and neck, like a hot water bottle or heating pad, or very warm tub baths, and it'll give temporary relief. If you become quite concerned about your neck, you can buy a soft neck collar at the pharmacy to wear for a while when you're up and about, it will keep your head from moving around too much. You can also put your right arm in a home-made sling with an old shirt when you go out, to keep your arm from tugging on your neck. Also, ask a friend or relative to gently massage your shoulders, really helps when you have injured your upper extremities and neck. Try to rest as much as you can, until you speak to the doc about your neck pictures.