Neck pain is possible but uncommon after cochlear implant surgery. To perform the surgery safely, your head was likely turned away from your implant ear. This can cause some temporary stiffness. Rarely muscle tension can develop after ear surgery, but before settling on that as the answer, it would be important to rule out other common sources of neck pain, as it’s possible that they are unrelated. Similarly, prolonged dizziness can happen after cochlear implantation, but unrelated as well. Talking to your surgeon about specifics (type of dizziness, time course, degree of severity) would all be important to start to understand the relationship.