C.K.
There is at least one chiropractor who posts on here, and I will be interested to see what she has to say if she responds.
I think you should definitely go back and see your chiropractor and explain what happened, but I'm not so sure you will be able to get a "free" adjustment. First, you need to find out what happened and hopefully he will be honest. Maybe your neck was worse off than normal before he adjusted. Maybe he did something slightly different, and now your body doesn't know how to react. (I have had "difficult" adjustments but my chiropractor has stated that that was the case and then told me to expect to be sore as my muscles got used to being "in place" again.) In any event, it's worth going back and talking to him face-to-face. I'm sure he values you as a client, and you obviously need further treatment.
Regarding the free adjustment, you can certainly ask, but we have to keep in mind that the human body is complex, not necessarily black and white. We are not talking about a mechanic doing bad repairs on a vehicle. Think of all the ways things can go wrong w/an MD (allergic reaction to a prescription, wrong diagnosis) and rarely do we think to ask for free medical treatment in these cases.
You raise an interesting question, though. In any event, I hope you get this resolved and get back to feeling better.