The solo student pilot reported that, while landing in a crosswind, during thunderstorm activity, she feared that a go around would put her into the storm. She added that the airplane bounced during the initial touchdown. She then applied "a bit of power" to recover, but the airplane porpoised, and the nose landing gear collapsed. The airplane sustained substantial damage to the engine mount. The director of flight operations for the flight school reported that, the student was endorsed for the solo cross country, she had received a weather briefing, and that she and her instructor had a briefing and discussion of the airfield and weather before her departure. He added that, she was supposed to arrive before the summer storms started, but the storms came early. The student pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation. The automated weather observation system at the accident airport reported that, about the time of the accident, the wind was from 140° at 15 knots. The student pilot landed on runway 10R. The observation further indicated thunderstorm activity and cumulonimbus clouds with occasional lightening in cloud and cloud to ground.