A220 pilot reported aircraft pressurization system malfunction during departure. Flight diverted and after landing manually adjusted cabin altitude before opening aircraft doors.

Narrative

Upon departure from ZZZ; the flight crew noticed an unusual amount of pressure changes that caused us to constantly 'pop' our ears. As we continued to climb toward our cruise altitude; the issue continued but was more mild and intermittent. When we reach cruise; the cabin called us to report a passenger complaining about a loud 'squeal' from the exit row on aircraft right. At this time; we started closely monitoring the cabin pressure and noticed the CAB ALT fluctuating +/- 800' and RATE fluctuating +/- 1500 with a DeltaP ranging from 8.2-8.6. This situation continued and was causing the flight crew ear pain and headaches. After reaching out with Dispatch; Maintenance; and the cabin; we decided to error on the side of caution and protect our passengers from further discomfort by diverting to ZZZ1. As we descended for approach; the constant ear 'popping' and discomfort returned; similar to departure; and when established on the approach the CAB ALT became -2000' and remained until parking at the gate. During taxi in; we warned the ground crew to avoid opening any aircraft doors until we figured out the best way to reduce the cabin pressure. When parked; we MANUALLY increased the CAB ALT to achieve a DeltaP of zero before finally opening the doors and giving our passengers relief.