It might not be possible in such a short period of time, there's not enough time to plan or give an event. The best possible thing to do at this time might be to put together a package with a cover letter explaining why you need the money, what it will be used for and asking people to contribute what they can. It may not be enough time to create a website, but you can create a myspace in an hour, add a link to a paypal account and you can include it in your package. You can email different companies, even walk into different companies and ask for the manager. Be prepared to show proof of what you need and why you need it, as well allowing them to pay the hospital or doctor directly, since many people are wary about just giving away money. Talk to your local newspapers and tv stations and find out if they are interested in covering it as a story....if they are, and they mention your website, myspace, or even the hospital where they can make donations. Let me know if you have any questions
Any business is approachable, from the smallest dry cleaner and sandwich shop, to such companies as Walmart, Kmart, McDonalds, etc. Some of them will refer you to their corporate offices, and you can follow up with them. It's the smaller businesses that may be more willing to write a check. Talk to your local museums, churches, etc, to find out if anyone would be interested or able to help you raise money. Your package should include the story, pictures of the child, and what you need. Again, you'll want to offer them a way that they can pay the hospital directly. You will also want to reach out to your local news station, newspapers, magazines, radio stations, etc. If they can do a story on it, it can encourage people from the community to send in money.
Let me know if you want to talk more