C172 pilot reported a runway excursion and equipment issues.

Narrative

Student pilot practicing touch and go approaches at ZZZ. Clear day. Initial ATIS wind 070@4. Directed by ATC to use Runway XXL; left pattern. Two touch and goes; and one go-around prior to the event. I was specifically working on energy management on landing; as I had been finding myself routinely high and fast; leading to extended time over runway to bleed off excess energy. The go-around prior to the incident approach was due to being too high on approach. One factor of note is that the north runway at ZZZ is comparatively short; and given the specific skill I was practicing; I was very mindful of needing to get back in the air quickly or have low threshold for go-around. On final circuit leading to event; ATC was managing an incoming helicopter approach and extended my downwind. When turn to base was approved; I completed turn to base and started a descent. Turned to long final and on a good glideslope. There were some notable updrafts that left me again high; so reduced power; added full flaps; and was back to a stable but steeper glideslope. I noted that tower had informed incoming helicopter that current winds were 050@9kts. Landing was unremarkable. Crossed threshold at approximately 60kts and had fairly smooth landing in first stage of runway though slightly left of centerline. At this point I re-applied full power and glanced down to the flap handle to raise flaps. Felt plane start veering to the left. I was already applying right rudder crosswind correction; and additional rudder due to being left of centerline. I do not specifically remember applying further correction for power but this is fairly automatic; and definitely added more correction when aircraft started veering left. I do not precisely recall subsequent events; but the aircraft continued to veer to the left and began skidding; leaving the left side of the runway in a right skid. I pulled back power at some point. Aircraft continued past the grass area and ultimately came to rest in a ditch along the runway. I had minor injuries (couple of abrasions). I am not certain of the extent of aircraft damage at this point; but I do know that the nose wheel was sheered off and the propeller hit the dirt. Reviewed the case in my mind and with CFI; and I was also able to get information from the state troopers who investigated the scene. My perception was that a gust was lifting my left wind and the aircraft was turning into the wind; but that additional rudder input and crosswind correction was not correcting. The wheel skid evidence actually showed heavy loading on the left main; indicating that the wing was not being lifted and actually probably pushed down by crosswind correction.In reviewing with CFI; I believe the following factors contributed to the event.1) I applied power very quickly after landing and more rapidly than I generally apply power. This was driven by a pre-set perception of short runway and need to get speed to take off; but may have lead to a mismatch in p-factor correction vs power application. 2) Due to the flaps still being down when power was applied; I likely unloaded the landing gear; reducing effectiveness of the nose wheel in helping to correct for the leftward turn.3) There are buildings (and the helicopter pad) to the immediate north-east of the runway. Given wind direction; it is likely that the first part of the runway had stable winds; but the later part of the runway had more abnormal gusts and eddies caused by wind at the time flowing over those structures. I feel it is likely that a gust effect in combination with p-factor effect and further exacerbated by full flaps being down and catching the gusts contributed to the rapid left turning force on the aircraft; while power application unloading the wheels reduced the ability to correct for this.4) As a final point; I was specifically focusing on the quality of my landings. While I had mentally briefed the relative shortness of the runway; effect of temperature (hotday) on aircraft performance; and consideration for need to make an early abort / go-around decision; I was ultimately thinking about the landing; not the subsequent take off; which I think impacted my response time and speed to the event.Potential corrective actions:1) Personally: this is a very important lesson in making slow changes to aircraft state; not feeling rushed and always being willing to just abort a take off. Also the importance of order of operations. While the flaps would have taken a moment to come up; the relative loss of lift and loading of the gear may have allowed for better control.2) Environmentally; the ditch along the runway halted the aircraft; but without this ditch running along the runway; this event would likely have been a runway excursion into the grass but with very little actual damage to the aircraft. Consideration of space around runways particularly around facilities that have significant training traffic with inexperienced pilots who are more likely to make errors may be a useful consideration.