How do I prevent water from streaming into my driveway?
It looks like your land sits a little lower than the adjacent roadway. It would be a cost but if you pave the first 10 ft of your driveway you can make a little berm with that pavement. Since pavement is non-porous the amount of water to overcome a couple of inches of slope would be substantial. Yet those same couple of inches will not be much to drive over. You really only need 0.5% slope for a couple of feet. While your gravel seems solid it likely has enough space between the rocks for water to pass through. If there is storm sewer nearby you could also look into installing a trench drain. Though that would perform better if your driveway was paved. The water would have a tendency to go around the drain and wash out the soil at the edges. 
Some interesting links
Pennsylvania Code  has good stuff on the driveway slopes. This picture is from their site.

This is a trench drain.