I’m sorry to hear about your injury. It is good that you do not have any neurological symptoms. The most common cause of neck and back ache in an otherwise healthy young individual is a muscle strain.
However, with the background of a traumatic incident, the first thing I would recommend would be for you to have your neck screened to exclude any possibility of an injury such as a fracture or a ligamenteous strain.
The best way to do this is to see a health professional to get a full physical and neurological exam, and an opinion on what further investigations are needed to evaluate your condition.
After evaluation and exclusion of any worrying injuries, a simple neck sprain or muscle tightness can be treated with a short course of painkillers and physiotherapy.
This would take some time to recover and get back to normal function depending on the extent of injury (a simple neck muscle strain might take anywhere from 2-6 weeks to recover).
Hope you feel better soon, and I wish you all the best with your recovery!