Basic sunscreen is zinc. To get that into an applicable form it is usually put into an oil suspension. As mentioned you don't like the oil. You can also get alcohol based suspension sunscreens that feel a lot nicer; and sunscreen in spray form. The benefit of oil is that it doesn't wash off so easily. But there's no point being stuck with oil based sunscreen if they make you feel that uncomfortable

This link might help: http://www.skinacea.com/sunscreen/physical-vs-chemical-sunscreen.html#.VdunDbKqqko as should https://en.wikipedia.org/wiki/Sunscreen