Car accident 3 weeks ago, doctor in the er diagonest neck sprain but now the pain in my neck just is getting worse every day, is that normal?

Not normal: Neck sprain should be getting better not worse. I your symptoms are getting worse you should see your doctor for an exam and likely get a mri.

Yes: With the adrenaline still running through your body after the injury, that can dull the pain. As the days go by, it is very common to have increased pain, then as you treat it, it will slowly start to improve. Good luck, get well soon.

Whiplash injury: Is a common condition after car accident. Trauma may involve the cervical spine, especially in an acceleration-deceleration (whiplash) injury. The soft tissue structures of the upper quarter may develop myofascial trigger points that are capable of referring pain to the head. It is possible that injury to the temporomandibular joints (tmjs) can follow direct trauma. Rec.: see pain management doc.

It may or may not be: Sometimes after an injury, muscles around the area injured can become irritated and go into some spasm. This can result in pain with motion that seems to worsen over short time. If this is the case, i would recommend seeking care from a physician who may be able to better determine if the pain is "normal".