Student pilot reported they lost control of the aircraft landing in a gust of wind resulting in a runway excursion and prop strike on their first solo.

Narrative

It was morning at ZZZ. METAR stated clear skies and calm winds. I did two warm up laps in the XXL traffic pattern during dual flight training with my instructor in a Cessna Skyhawk 172. We noticed some turbulence on the downwind. My instructor was happy with my traffic pattern flying and cleared me for my first solo flight. I dropped my instructor off and followed ATC instructions to rejoin the pattern. PIREPS are coming in the radio for turbulence and some crosswinds for Runway XXL and XXR. I felt a strong wind push from the right drifting me off my course on my takeoff and upwind leg. I fly the pattern as usual with not much issues. On my final approach into Runway XXL I caught myself thinking about how I am now 100% responsible for this landing and my instructor is no longer around to get me out of small mistakes that can turn into big ones. This sparked some fear in me as I approach the runway and clouded some of my decision making skills. Regardless of the crosswind giving me a harder time keeping my centerline with the runway. I still felt my approach was stable. I believe towards the start of my round out; I over compensated for the right pushing wind and ended up too far to the right of the runway.I noticed this and I began correcting to go back to centerline so I added left rudder input. I had to begin my flare but the nose of the plane was still facing too far to the left. I again correct for this by adding right rudder but by this time I was touching down. As soon as the wheels hit the ground the plane veered to the right hard. I feared that I would deviate into the parallel Runway XXR and instinctually slammed on the brakes causing the propeller to strike the runway. I release the brake to correct for this and the plane started veering to the left. I add right rudder input but due to the stressful situation. I mistakenly depress the right brakes which causes the right wing to dip down. I release the right brakes in fear of the wing striking the runway and catching on fire. In doing so the plane continued to veer left and ran off the runway. I was able to avoid all the runway lights and indicators and came to a full stop in the gravel area in front of Tower. I performed emergency shut down and exited per ATC instructions. Aircraft X sustained damages to its propeller. I checked the METAR after the flight and the winds were no longer reported calm and showed variable. Thinking back I wish I would have aborted the landing when I was too far to the right of the centerline. I could have set myself up for a more centered landing having a better idea of the wind conditions. Secondly; I realize I need to work on rudder control on touchdown and rollout. I need to train myself out of defaulting to the brakes in a situation like that. Had I stayed off the brakes and made small corrections with rudder and ailerons. I might have saved that landing.