PA-28 pilot reported flying an unstable approach and executed a go around that resulted in a prop strike that was noticed after landing.

Narrative

This was a solo flight operation to ZZZ and back. After contacting the tower at ZZZ; was cleared for a straight in approach rwy XX. During the approach; had to make power changes to maintain altitude and airspeed as there was no visual aid like PAPI available for the rwy. Engine parameters were in the green during the approach. Airspeed was kept at +5kts to adjust for the gusting winds.The aircraft was setup in the landing configuration and the before landing checklist was complete. Over the threshold; the aircraft became unstable and by the time the go around was initiated; the aircraft had touched down and bounced.The go around checklist was complete and requested ATC for another lap in the pattern. Engine parameters were in the green. There were no changes noted in the sound of the engine nor any vibrations. Normal traffic pattern procedures were followed and the aircraft was again setup in the landing configuration with the checklists completed; a safe landing was made on rwy XX.Taxi was requested back to the active; during taxi there was momentary drop in the oil pressure however; it went back to the normal range shortly. At the hold short for rwy XX; the line up checklist was completed and the engine parameters were in the green - oil pressure; rpm; fuel flow and egt.A normal takeoff was performed from rwy XX and returned back into ZZZ1. Climb checklists; cruise checklists were performed during the appropriate phases. The engine parameters were in the green. A go around was made at ZZZ1 XYL once before making the final landing on XYL.After the parking checklist; during postflight inspection the aircraft was tied down; the landing gears; nose gears - tires and struts were checked. The hook on the tail was checked for tail strike. However; visual inspection looked normal and no abnormalities were noted at that time.The prop strike was discovered later by the ground crew after flight.What could have been done better/corrective actions?* Earlier go around could have been executed for unstable approach. Power adjustments could have been minimised.* Stop at ZZZ for inspection of the bounced landing and call maintenance if abnormalities were discovered at that point in time.* Check engine and prop during the post-flight inspection at ZZZ1.