I'd go to the chiropractor. I get the same thing, and just need my neck adjusted. As for the "snapping and cracking," that is not a professional term nor a professional method. There are various ways to do spinal manipulation, and there are different methods, depending on the chiropractic physician's treatment, schooling, your personal feelings, what is wrong, what needs to be done,...some people prefer activator methods, there are certainly more "gentle" approaches, and more aggressive approaches. But they are not carelessly "cracking and popping" like a person does to their own knuckles. They are schooled in precise manners in which to mobilize and manipulate the spinal joints to bring about relief.
It's like comparing a surgeon cutting with a scalpel with cutting yourself with a kitchen knife. There's a huge difference.
Neurological involvement will often cause the numbness you're talking about. Depending on which level is out, you can get it on the outer 2 fingers, like you have, or on the inner 3 fingers. There are unique pathways which help identify what area if your neck might be contributing.
I wouldn't rule out the possibility of the ulnar nerve being affected, though, because that could most definitely contribute.
What I personally like about chiros is they aren't going to inject you with needles or give you drugs, - their approach is non-invasive and addresses structural integrity issues, not symptomatic-only relief.