C172 pilot on a solo cross country reported the loss of control while intending to complete a touch and go. There was a cross wind at the time of the incident. The aircraft departed the runway and the prop of the single engine aircraft struck a taxiway light. The trainee taxied to the ramp and called the CFI for assistance. There was no other reported damage to the aircraft.

Narrative

On Day 15 a student solo cross-country flight was planned as partial fulfillment of Part 61 training requirements towards my private pilot certification. This report is a description of events that occurred before; during and after this flight.The objective of this solo cross-country flight was to fly from ZZZ1 to ZZZ2 assisted by flight-following; with one landing at ZZZ en-route between the departure and destination points.A similar dual cross-country flight (student and instructor) had previously been successfully completed on Day 0. This Day 0 flight took off from ZZZ1; made a full-stop landing at ZZZ2; then departed to ZZZ3; made a full-stop landing and a subsequent takeoff from ZZZ3; Then flew to ZZZ where a touch-and-go maneuver was performed; and finally terminated at ZZZ1. This was followed on Day 14 by a student solo cross country round-trip from ZZZ1 to ZZZ4 which was successfully completed.On Day 15; the original plan was to fly solo directly from ZZZ1 to ZZZ2 overflying the reservoir via ZZZZZ and then return to ZZZ1 with one landing en-route at ZZZ. This would be very similar to the previous dual-cross country flight to ZZZ2 except without a stop at ZZZ3.On that day; low clouds persisted around the reservoir/ZZZZZ area into late morning. Meanwhile; skies south of ZZZ1 were less cloudy which offered a better chance of crossing the mountains.With the expectation that air traffic patterns around ZZZZZ would likely cause ZZZ Approach to issue altitude restrictions of 4;500 ft. - which meant overflying these clouds might not be an option - and with the desire to avoid any chance of encountering a scud-running scenario between the low clouds and the mountains on this VFR flight; it was agreed to modify the direction of the outbound flight and head southbound to ZZZ en-route to ZZZ2. While clouds were present south of ZZZ1; they were scattered; and altitude restrictions were less likely to be encountered; which meant that overflying these clouds would be a viable option. I was advised that while three landings would be needed to satisfy the cross-country portion of the Part 61 training requirements; a touch-and-go at ZZZ would be sufficient to meet this requirement.A flight-following was requested on this trip during initial contact with ZZZ1 Ground. Upon completing all pre-flight and run-up checks; takeoff from ZZZ1 occurred at XA26. Upon transfer from ATC to ZZZ Approach; I was told that altitude would be at my discretion which meant I was free to overfly cloud cover over the mountains south of ZZZ1. I climbed to 7;500 ft. altitude and remained there until I was around eight (8) NM west of ZZZ. I had switched over (with authorization) from ZZZ Approach to ZZZ CTAF a few minutes before I began the descent into ZZZ; and at around 1;100 ft. MSL I commenced the 45-degree entry into a left traffic pattern for Runway XX; which I entered at 900 ft.The winds at ZZZ as I approached my short final was from 280 at around 9-10 kts. The wind direction was re-verified after landing and when the aircraft was parked. This 40-degree crosswind did not pose a major challenge; and with sufficient crosswind correction I landed on Runway XX safely and in full control of the aircraft at XB04. Once the aircraft was safely on the ground and rolling along the runway centerline; I commenced the touch-and-go procedure. This involved focusing on (1) carb-heat; (2) trim; and (3) flaps - in that order; with flaps intending to be retracted only once airborne with sufficient airspeed; being mindful of Vfe - while ensuring sufficient right rudder to offset the left-turning tendency of the accelerating aircraft. However; in the heat of the moment while focusing on ensuring proper trim so as to prevent an excessive pitch-up tendency; insufficient right-rudder was applied during the acceleration; which caused the aircraft to swerve to the left; which in turn caused a loss of control. As it became clear that I would be unable to maintain directional control and stay the course along the runway; I aborted the takeoff and turned my focus on ensuring that the aircraft continued to maintain proper attitude and did not tip over at any point. As the aircraft swerved to the left; the propeller hit a blue taxiway light at the intersection of the runway and the diagonal taxiway. The aircraft continued to roll over the grass and re-emerged onto the taxiway at which point I slowly taxied the aircraft to the end of the taxiway; turned around and taxied it into nearby a parking spot. After the aircraft was secured; I contacted my CFI; notified him of the situation; and sent photos of the propeller strike. Further inspection revealed that there was no other visible damage to the aircraft; and all lights; control surfaces; and the aircraft hull appeared intact. Due to the propeller strike; it was determined that the aircraft was not safe to fly and so I awaited further instructions from my CFI who arrived later in the day from ZZZ1 to pick me up. The aircraft was tied-down at ZZZ and we left a note with airport operations; as no airport management personnel were around anywhere in or around the airport on that day.Although my student pilot certificate was issued in late last year; I never received it in the mail to date. Upon calling FAA on the day following the event; I discovered that it was returned to the FAA as undeliverable on account of FAA incorrectly addressing my mail to a non-existent street address (typo). I was told the certificate would be re-sent to me in a few weeks.Several lessons can be learned from this experience and this will be the topic of conversation; reflection and introspection in the coming days and weeks. It is clear that things could have been done differently - for example; more practice could have been undertaken before a solo touch-and-go attempt - and better expectations; communication and clarifications can be developed between student and teacher when agreeing upon a flight plan and strategy. Hindsight however - as they say - is 20/20. The hope is that such painful mistakes can be avoided in future.