Light aircraft pilot reported a near miss with a helicopter during cruise while under VFR flight following with ATC.

Narrative

Near miss with a helicopter conducting air tour flights of the Chicago lakefront. My tail number was XXXXX and I did not get the helicopters tail number. I was using VFR flight following with Chicago approach and had passed the helicopter when I was flying southbound. At 7.5 miles 070 radial from MDW I turned to the right back northbound along the lakeshore. Approached called out traffic 12 o clock; .5 miles same altitude opposite direction. I thought I had the helicopter traffic in sight and advised ATC but I actually had traffic 2 miles; 12 o clock same altitude opposite direction. ADS-B showed the helicopter further east of me heading southwest so I evaded left of the perceived traffic. I decided to us non standard traffic avoidance because I did not believe a right turn would allow for traffic clearance from the airplane traffic I mistook for the helicopter. After ADS-B showed the passage of the helicopter traffic it showed altitude -300; and I realized that the traffic I had in sight was another airplane opposite direction. I never actually saw the helicopter and am unsure how close the near miss was. On ADS-B the helicopter never appeared to evade me. They were not using flight following.