I've never done the exact same thing, but often run to/from work, which has similar problems. I wear a backpack with my clothes for the day, breakfast, lunch, wallet, etc, which sounds a lot, but is actually fine.
I've got a dakine rucksack, which is quite small, padded, and very comfy. It can be a bit of a pain on days when I've been disorganised, and forgot to leave my hairstraightners, toiletries, makeup, etc at work the night before. But as long as I keep the stuff I'm carrying to a minimum, I barely notice it.