The most common negative side effect of having chiropractic care done to you is mild soreness in your upper back, neck or low back. I would suggest that this type of soreness is due to spinal manipulations effect of increasing range of motion in hypermobile areas of the spine.
If your spine has not been moving well for some time, it may not be used to having a full range of motion. Suddenly restoring more movement in a certain body part can reawaken nerve endings, including pain sensitive nerve endings or movement sensors, and this can confuse the nervous system, and make you sore.
Researchers from Penn State, Loma Linda University Medical Center, and the Pennsylvania state university conducted a systematic review and meta-analysis of chiropractic neck manipulation and cervical artery dissection, and they found no convincing evidence to support a causal link. -Church, et al (2016) Cureus
A study published in 2015 in the spine journal found that, "among Medicare beneficiaries aged 66 to 99 years with an office visit for a neuromuscular skeletal problem, risk of injury to the head, neck, or trunk within seven days was 76% lower among subjects with a chiropractic office visit then among those who saw a primary care physician." -Whendon et al (2015) Spine
Kosloff et al found the significant association between chiropractic care and the risk of stroke. They concluded that manipulation is an unlikely cause a stroke. The positive association between primary care provider visits and vertebral artery stroke is most likely due to patient decisions to seek care for the symptoms, which are headache and neck pain, of arterial dissection. In other words arterial dissection in the neck can cause neck pain, and this can cause people to seek out care from either a medical provider or a chiropractor. The symptoms are present and the dissection may also be present well before the patient decides to seek care. They concluded that using chiropractic visits as a measure of exposure to manipulation may result in unreliable estimates of the strength of association with the occurrence of vertebral artery stroke. --Kosloff et al Chiropractic Manipulative Therapy
Because of the dangers of taking opioids for pain, new guidelines from the American College of Physicians (ACP) recommend that clinicians call for non-drug therapy as a first approach in the treatments of acute, subacute, and chronic low back pain. They recommend that clinicians and patients should seek non-pharmacologic treatment with superficial heat massage, acupuncture, or spinal manipulation.
The ACP guidelines state that "exercise, rehabilitation, acupuncture, and spinal manipulation are shown to improve symptoms with little risk of harm." It is only after these modalities are found that to work that physicians and patients to discuss medical-pharmaceutical care for back pain.