I think you'll be okay, but only you can be the judge. Normally first periods are super light, and despite everything people say, you can actually get away with a lot if you're having just some staining and maybe a little more. I went swimming once with my period because I had no other options and it ended up being okay. A tampon is your best bet, but it's so hard to do that while you're rushed and in stress, especially if it's your first time! If you can, stop by any drugstore and pick up some small winged pads. But if you cant, I say wing it, and just go to the bathroom whenever you have the chance and clean yourself up. I highly doubt there'll suddenly be some big embarrassing whoosh if this is your first one.