It's not normal for the hood to rise like that. While raising the little rubber pads on each front corner will tighten things up, it could just hold the hood up too high.
You should be able to simulate this while parked to figure out what's going on. Maybe the latch isn't securing the hood properly, in the fully closed position. Maybe it got knocked out of adjustment somehow? Maybe something is bent or broken in the hood, core support or latch setup?
I'd want to know exactly what's going on before driving it more. I've had a hood fly up while driving, luckily on a junker at low speed, but you really want to avoid this event.
The surface from the fenders, above the lights, and onto the front of the hood should be relatively level as it transitions from fender to hood both when parked and driving. The hood should latch in two positions. An initial position that is just the hood release handle, under the front edge of the hood, holding it down and the 2nd position the fully closed position that requires the hood release below the steering wheel to be pulled.
Totally different issue, but if the hood is raising or fluttering in the middle then the adhesive between the inner structure and the outer skin has failed. That's a common issue and relatively easy to fix though again, it's not related to the front-edge of the hood staying securely in position after the hood has been fully closed.
Good luck.