Student pilot flying C-172 aircraft reported a runway excursion on landing.

Narrative

Coming in for a landing at ZZZ; student was slightly high and planned on landing farther down the runway versus just as immediately as the runway allowed. Airspeed was 63 knots and coordinated. Student was over the runway and it felt like the plane got hit by wind shear. It was pushed down to the ground and also pushed to the left side of the runway. Being close the ground the airplane made contact; porpoised and the left wheel went off the runway by about a foot. Once stopped; tower asked if assistance was needed; the plane easily went right back to the runway and the student said to tower that no assistance was needed and they would like to return to ZZZ1 instead of completing the original plan to go to ZZZ2. The student then took off and communicated with the tower on what coordinates to fly. The flight back to ZZZ1 was unremarkable and the landing was good. Perceptions/judgments/decisions- the right course of action would have been to taxi in; after talking to the tower via the phone that was understood. As a student it would have been helpful for tower to say that versus just asking if assistance and leaving the conversation as is. Further; there's always the opportunity to go around if the landing isn't exactly perfect which should be recognized here.What could be done to prevent the problem- instead of being just a bit high; a go around would have been ok to do to come in at a more appropriate altitude. However the wind shear is something that is less avoidable and unknown when it will happen per the students prior instructor. More training on windy conditions would be helpful. Better communication with directions from the tower would also be helpful in an event like this.