3 weeks is not that long. But if you are being treated : adjustments, traction, stretching, ultrasound, electrical muscle stim and of course REST...then it should be at least 50-75% better in 6 weeks. If not you definately need further testing - preferably MRI and EMG (electromyelogram- it tests electrical nerve conduction to determine the extent and type of injury to nerves). MRI will tell us what , if anything, you have done to the disc. A ruptured disc can cause these symptoms.
Between every 2 bones (vertebrae) in the back there are 5 joints. The posterior joints are called facets - because they are flat (like facets on a cut diamond) and the bottom of one vertebrae and the top of the other fit together to allow movement. The facets are wrapped in a saran wrap (pastic cooking wrap) kind of material called synovium. When injured te synovium can swell with synovial fluid - kind of the way your finger swells up when you jam your finger. But typically this will cause pain on extension (backwards) of the neck. The swollen synovium and related inflammatory chemicals in the area can irritate the nerve endings causing inflammation of the nerves that then course down the arm. This is called posterior facet syndrome.
There is also a sock like sheath that covers the nerves as they first exit the spine, called the dura. The dura can become irritated and inflammed and cause nerve irritation too - like a sock that is too tight on your foot. Also causing neurologic symptoms.
All of these problems can and should largely resolve within 6 weeks on the upper most. If not then you should get further testing.
If your range of motion is uninhibited and non-painful (touch your chin to your chest, ` 80 degrees left and right rotation (basically your chin almost lines up with your trap, and 45 degrees lateral flexion (try touching your ear to your shoulder without raising your shoulder, and you can go about halfway) - then I myself don't think more adjustmetns would help - unless there is focal restriction at just one motion segment in the neck. But most rotation occurs between the first and second vertebrae around what is called the odontoid. The odontoid is a toothlike/spikelike process sticking up off the 2nd vertebrae around which the first vertebrae rotates.
You might also have actually injured a spot lower down - between the shoulder blades, and be suffering from something more akin to what is know as thoracic outlet syndrome. You can injure the first few thoracic vertebrae (disc, facets,dura) and get the same symptoms. Make sure you mid back between the shoulder blades is also getting aligned.
Also if your traps are large (too large?) and pecs too tight it can cause the symptoms. Large traps can compress a bundle of nerves called the brachial plexus that exit the neck and go down the arms. Be sure to work the rhomboids enough to pull the shoulder blades back and down to release the pressure the traps can cause on the neck.
Excessively tight pecs can also pull the shoulder blades and arms forward anc compress the nerves - the brachial plexus exits the neck, kind of goes through the arm pit and down the arm. Tight pecs cause a squeezing near the armpits and compress the nerves. I like a stretch Dogcrapp recommends on animals board of lying on a bench holding 15 LB dumbells letting it stretch your arms to the floor.
Sorry if that gives you too much to think about.
If you severely, and I mean severely damaged the nerves, then they will first decay sort of, undergoing hat is called Wallerian degeneration - in which the nerve breaks down and then regrows. But that is very severe nerve damage. This might take months. The nerves and brain are made up 80% of a fatty acid (Omega 3 fatty acid) called DHA. Salmon oil is made up of EPA/DHA. I believe taking omega 3 fatty acids containing DHA will help the nerves repair faster - although no conclusive studies would prove this yet.