C172 student pilot reported loss of control on crosswind touch and go which resulted in runway excursion and prop strike.

Narrative

I have 49 flight training hours; with 5.7 hours of training in crosswind conditions. I was flying my first solo cross country flight to ZZZ1 from ZZZ. I had my first solo on Day 0. I have a total of 2.9 solo hours. I have flown a cross country flight to ZZZ1 once before. I landed on Runway XX. The winds were from the direction 240 at 10 kts. I approached with the intention to go around if anything doesn't feel or look right. The crosswind was coming from the left side of the aircraft; so I used left aileron and right rudder. The approach felt perfect and I landed on centerline and aligned straight with the runway. As I cleaned up the flaps and applied throttle for a touch and go; the plane started going towards the left side of the runway; opposite of the wind direction; it appeared to be a weather vain. I kept the left wing down and applied full right rudder. I continued towards the left side of the runway; so once I was at the grass; I pulled the throttle to idle and eventually stopped in the grass to the left off of the runway. There were light prop strikes in the dirt; but no dents on the prop; nor damage anywhere else on the plane; nor to myself.