I'm going through something similar with a family member having MS and I'm currently in law school. Although I didn't face as pressing of a concern as you do, what with having to consider covering multiple people's expense, there was a huge concern that my money was going to have to be siphoned off to cover medical and other expenses. The situation has turned out to be much better than I thought, so here are a few things I did that perhaps might work for you.
1. Ask the school for a scholarship or other free money, explaining your sudden situation (you have nothing to lose).
2. Look into a Special Needs Trust in a state where you could reasonably expect your family to be, whether that is their current place of residence or where you will be in school. It doesn't sound like your family has much in the way of assets, but what such trusts do is allow you to liquidate everything the trustor owns (in this case your dad), still qualify for full Medicaid, SSD, Medicare, etc. This should cover all medical costs (with the dual eligibility of Medicaid/Medicare, especially if you can find a care team that accepts "assignment."
. All of the money in the trust will go to quality of life stuff, medical and other things will be covered by the gov't. There are downsides to this, but it's a huge help.
3. Even if it has to come out of your own money, hire a Life Care Planning Elder Law attorney. There are some through this organization
, but I know there are other similar groups. Think of what these people can do as estate planning for fucked up life situations. It has been a huge help in the process for me. They can handle any Special Needs Trust stuff setup, approval for gov't benefits, the works. Sure you could drudge through the whole process, but I don't think it's as simple and timely as it has been made out here in other posts. This also lets you keep your distance and focus on your life, which is easy because it sounds like you're like me and aren't overly emotionally involved, just trying to do the right thing while taking care of yourself.
4. Definitely get in touch with the MS Society.
5. Consider assisted living or in-home care for your dad. Depending on the interplay of my mentions above with state law regarding Medicaid, these could be free or hugely discounted.
6. Go to law school, you'll be doing your family the biggest benefit by being able to make a serious income to supplement these things down the road, if need be.