Pilot reported an NMAC event during initial approach which caused a lingering distraction resulting in a landing without a landing clearance.

Narrative

On initial handoff from approach to ZZZ Tower prior to entering Delta airspace I was given instructions to maneuver for a right base to Runway XX and advise when 2 miles out. At the time I was NW of the airport flying SE. I was also advised that there was an aircraft departing the airport to the NE. On my screen I saw an aircraft departing the airport moving eastbound; so I didn't think he would be a factor. As I entered Delta airspace; descending to pattern altitude; I was reviewing the approach/descent checklist and configuring the airplane for landing when without warning I saw what looked like a 172 fly what seemed like 100 feet above me heading north. Before I even had time to register what happened; he already passed me overhead.In retrospect I think this is what made me lose my focus and forget to make my 2 mile call. I then proceeded to perform my right base pattern entry and landed without incident but without having obtained a landing clearance. After shut down I called the Tower and apologized for my transgression and informed him of the near miss.