I would say that with all things you're allowed to be skeptical.
From what I'm looking at, however, your position is fairly neutral. A lateral "flexion" view would demonstrate more movement in the upper cervical region -- which isn't evident in the picture you've displayed. Although, I'm of the opinion that neutral lateral cervical views, like this one, should be taken seated, not standing.
Your disc spaces are acceptable and there's minor arthritic degeneration present. The two primary problems visible to me are the reduced cervical curve and the inferior atlas plane line (which may only be due to you tucking your chin in).
With that being said, a healthy cervical curve is really important. It's generally 42-degrees, and while I didn't measure yours, it appears close to 0. That in and of itself needs to be improved -- the sooner the better.
Can cervical misalignment cause nerve irritation and arm pain? Absolutely. I would say that chiropractic care is certainly worth pursuing. Give the doctor 4-6 weeks and let him/her perform a progress exam after that time. If objective improvements can be measured, then you're in the right place. If not, it's perfectly acceptable to seek care elsewhere.
If you'd like to receive precision, laser-aligned x-rays, I'd recommend visiting an Upper Cervical specialist (www.UpCspine.com). These doctors use head clamps, special chairs, and tilting x-ray buckeys that greatly minimize distortion and reduce positional error.
Adam Tanase, D.C.
www.drtanase.com