Before going any further, the best piece of advice would be to contact your chiropractor directly and ask him or her this question. Depending on your prognosis or what injuries or issues you might be facing, your doctor might have a very specific amount of running in mind that they feel is safe for you to do. Before you do anything else, it would be best to simply ask them directly.
Your current health, running experience, past injuries, and potential future injuries should dictate how far and how long you run each week. Without knowing exactly what your chiropractor would say, it does sound like you might have a history of a hurt back or spine. These injuries can range from chronic nerve pain that seems to never subside completely but is manageable enough to work though and run through sometimes, to a back injury that is just so painful every time you go out for a run that you might need to consider looking for alternative forms of exercise. I would advise, as a general rule of thumb, to air on the side of caution and always take it slow, especially when you are first starting your run and are not as warmed up. Be sure you build in plenty of time to stretch and warm up before you run, and time after to cool down. This will help ensure you don't injure yourself even more. If you start having intense pain at any point, immediately stop. If you are able to run consistently for any amount of time though, then I would start by running every other day, just a few miles as you regain your strength and build your endurance back up. Avoid high intensity workouts with a lot of jerking around, as well as any back weight bearing exercises. And try to tune into your body, perhaps more so than you are used to. Always, always focus on good form with good posture. When working through a painful injury, it is extremely important to know your body, and signs of fatigue, too much physical stress, and exhaustion. You will likely know when you are about to risk really hurting your back, as pain starts to intensify and you lose proper form.