Dry shampoo! It's great for greasy hair. My hair is dark so I use one which is specifically for brown hair (so you can't see any powder). Depending on how long your hair is, I personally do two french braids to keep my hair off my face entirely. Then I use a hand band, to make double sure. It sounds annoying but I'm used to it now. When I gym with my hair like that I don't actually have to dry shampoo it since none of my hair touched my face.
For my face I just use Simple moisturising face wash, followed by their toner and a Nivea face cream. I exercise in the morning so just wash after my workout and go to the gym without washing my face. No one actually cares what you look like in there so I don't feel self conscious.
I hope this helps. I know how annoying it is. I do see a lot of girls in my gym use face wipes before they get the shower so maybe that'd work for you? I presume they then wash it properly under the shower but obviously I don't know....