It's a myth that if you touch up foundation or powder it will always look cakey or cause break outs. I've read the following advice in a Japanese magazine for hot days and oily skin, and it's helped me a ton.
1. This is optional, but you can give your face a light spray with some sort of moisturizing liquid, ie. Fix+. This helps revitalize your skin and give you that lovely dewy look.
2. Blot with a tissue. If I skipped step 1, I just start by blotting with some blot paper if I have it, a tissue if I don't.
3. Since my foundation/powder/blush has somewhat worn off during the day, it's ok that I'm blotting it away and removing excess oil. If you find that all the oil coming off also takes off your foundation, don't worry, because it's better than touching up over oil that's been mixed in with your face make up. That creates cakiness.
4. Invest in a good concealer to touch up the trouble spots that have peeked through under fading foundation. You can use a Q-tip to gently clean away old foundation if you want, to apply a fresh dot with new concealer so that it doesn't cake on as much. I don't find tihs necessary usually since my face make up is never so heavy that by touching up it becomes cakey.
5. Invest in a good powder foundation (I like MUFE's all mat), because you can take it on the go with you and put it on again with a puff or a kabuki brush (I use a puff then blend out the powderiness with a fluffy brush). This will provide coverage, re-even out your skin, and also keep your oil at bay and under control and continue to blot out shine.
6. Reapply blush because you've just covered it up!
The above is just for face make up--I agree with above comments about just darkening your make up day to night with some darker colors.
I keep a lot of things in my make up bag, but if you don't have room for it, perhaps buy some duplicates of your home make up, and add a good powder foundation, and keep it all in your work drawer in a box/bag or in your school locker, whichever situation it is. That way you don't have to carry around a ton of product all the time.
If I'm going out and I may want to touch up, the most essential items are blotting powder I can fit a package of this easily in my wallet), a small stick concealer (I like Urban Decay's 24/7 concealer pencil), and lip product (including lip balm).