Upload & Sell: On
If you are on private property, you don't really have the right to even take pictures without permission, much less use them. But when you say "publish them on the web" do you mean as a part of a portfolio or on FB or for sale or ??
In general, photos taken in public (i.e., not on private property) can be used for art or editorial use without releases, but cannot be used for advertising (i.e., to promote a product or service).
If you do not have permission from the school, you very easily could be forced to take down your photos. You are a student and they have all the cards, if they don't grant permission there isn't much you can do about it.
Contracts are intended to ensure that both parties are on exactly the same page about such items as deliverables, schedule, payment, responsibilities, expenses, etc. Having a contract will prevent many if not most disputes, but won't "protect" you in court should someone sue you.
I suggest you read John Harrington's book "Best Business Practices for Photographers" or the ASMP publication "Business Practices for Professional Photography" to get an idea about how contracts, releases and all that work.