PA-28 student pilot reported a prop strike during landing procedure.

Narrative

I was approaching ZZZ on a solo XC. The flight was going as expected until I was within the Class D airspace for ZZZ. I was expecting ZZZ Center to hand me off to ZZZ Tower and never heard the handoff or I missed the call while trying to get the ATIS for ZZZ. I switched to ZZZ Tower asking for a full stop taxi back. I was cleared for Runway XX straight in on about a 6 mile final. From the ATIS and my preflight briefing I was expecting Runway XY so I was already a bit higher and faster than I intended to be. I committed to the landing instead of doing a go around and realized quickly that I was going to be faster than I expected and when I touched down the aircraft bounced back up off the runway. I tried to pitch up to hold it in ground affect until some of the speed would bleed off as I had a lot of runway left but the aircraft touched back down sooner than expected and bounced again. I didn't think I'd be able to add power back and attempt to retake off for a go-around so I committed to the landing. I bounced another time or two before the aircraft finally lost enough airspeed for me to taxi off the runway on the taxiway that Tower cleared me for.I didn't think anything of it beyond it being a much rougher landing than I expected. Tower asked if I wanted to taxi to the FBO or back to the runway for takeoff. I opted to taxi back for takeoff. Tower immediately cleared me to take off Runway XX and asked me to report clear of the airspace. I took off without incident and started my trip back to ZZZ1. I reached cruising altitude when I expected and flew back to ZZZ1 at 4500 MSL. As I neared the river I noticed the aircraft was descending slightly. I didn't think much of it since I was having to adjust the trim periodically to keep me straight and level. I increased some power to get me back to 4500 and continued the flight back to ZZZ1. Once within ZZZ1 airspace Approach handed me off to Tower and I landed on Runway YY without incident and was a very stable and clean landing. I taxied back to ramp per ATC instruction and proceeded with the shutdown procedure. I recorded tach and hobbs time and then proceed to grab my flight bag; iPad; and the binder we keep in the aircraft as part of rental checkout. I shut the door and immediately went to look for chocks on the chock rack where I normally expect to find them. There were none there available for the aircraft so I went inside to ask one of the instructors about it. I was told that if the FBO didn't leave any out to just leave it. I normally do my post flight inspection as I chock the wheels so I missed this part of my post flight when I went inside to ask about the chocks and never went back out. I proceeded to log my time in my logbook and wrap up some of the post flight check-in of the aircraft with the flight school. At this point one of the other members of the flight school came in and said that the propeller was bent on the aircraft. We went out and inspected it and immediately took the aircraft out of service for being un-airworthy and discussed what happened on the XC. After discussing the flight with some of the instructors at the flight school it became clear to me that I should have used my aeronautical decision making to immediately elect for a go around so that I could have a stabilized approach into ZZZ. I was flustered; nervous; and caught off guard when things didn't occur as previously practiced with my instructor and being embarrassed about my poor landing it never occurred to me that I could have had a prop strike as a result of the landing.