I would call your pediatrician just to be safe.
Before my DD was in gymnastics, I occasionally noticed petechiae around her eyes. One morning it was unusually pronounced, so I called her pediatricians office to ask them about it. The nurse I spoke with said they needed to see DD in office ASAP. Like, not in three hours, but right NOW. I started to freak out a little, and took her right in. They examined her and ordered bloodwork to be analyzed stat. They had her bloodwork results in like 20 minutes and said she was, thankfully, fine.
The dr. said that the two big concerns with petechiae are leukemia, and kids playing choking games. I think it's obvious that gymnastics could easily cause it as well, but if it is a new thing for your DD, I think you should double check with your pediatrician. The DD of an acquaintance was recently diagnosed with leukemia, and the symptoms were very subtle. Better be safe than sorry.