Helicopter Pilot reported a NMAC while transitioning through class delta airspace on a local transition route. The congested airspace and ATC workload were sited as contributing factors.

Narrative

I was operating a piston helicopter (solo) from ZZZ1 traveling toward ZZ2; transitioning through ZZZ Class D airspace. This is a common VFR route that is used by many GA aircraft. The route from ZZZ1 to ZZZ is along [a highway]; which is a bridge and causeway; running parallel with ZZZ3 Class B airspace. Before entering ZZZ class D airspace; I contacted ZZZ ATC about my intentions to transition through their airspace on the way toward ZZZ2. I was instructed to fly over the field at or above 1000 ft. At the typical point (toll plaza) I turned toward the Control Tower to fly over the center of the field. As usual; I ask for an altitude check and was told they saw me at 1000 ft.As I approached the airport; the ADS-B was starting to warn of 'TRAFFIC 10 O'CLOCK'. Just then; ATC sent a radio message 'TURN RIGHT; TURN RIGHT'; which I did. It was at that point I saw the aircraft at 10:00; approximately 200 ft. away fly past at 50 ft. below in a climb. If my position was one second later we would have intersected. As I was taking in what just happened; the ADS-B began to warn of other traffic; so I resumed my original course toward the tower. It appeared the ATC was very busy. I initially thought of yelling '[what] just happened?' but I just wanted to get clear of the airspace.