A M20 pilot reported on initial climb executing a go around from an unstable approach their propeller struck a runway light.

Narrative

This was a VFR flight (using flight following) with ZZZ as the destination. Once at pattern altitude; in close proximity to ZZZ; I started back towards the airport while completing my descent so I could enter the downwind on a 45. There were several airplanes in the pattern at that time; and when I shot my first approach; I was high and broke off the approach and went around. On my second attempt to land another aircraft joined the base leg without joining on the 45 to downwind for the runway. I think seeing that second airplane on base caused my ADSB to turn yellow and caused me some concern. I was a little high on final but on speed and I thought that I could bleed the speed off prior to getting to the threshold of the runway. This was not the case. I touched down about 2/3 down the runway. Recognizing that I was not going to stop in the remaining runway. I increased the throttle to max and rotated at VX. The airplane began to climb and that is when the airplane contacted the runway lighting. There was a sound of impact; but I thought it was the landing gear since no other anomalies existed and the plane was running smoothly. Wanting to have more resources available I made a command decision that a longer runway with emergency equipment available if I needed it with the perceived failed gear would be prudent. I contacted approach for a gear inspection and they asked if I could defer to ZZZ1; not thinking that there was a power plant or propeller issue I turned towards ZZZ1 airport. Contacting the controller at ZZZ1; he said he would take a look at my gear on a lower approach upon the inspection from the tower. After the low approach; he said the gear was down and I had no indication in the airplane that; it wasn't not. I landed the airplane on Runway XX and taxied to the FBO. Upon inspection at the FBO; the gear was fine; but the propeller was observed to have two areas on one blade that indicated it had contacted something. The aircraft is now at ZZZ1 for inspection and needed repairs.