G.day Allicat,
Go back to your specialist and ask him if he knows any facilities in Chicago area. I googled "cancer centers (American spelling!) chicago" and got a long list, some of which I had heard of. Get a letter from him to one of them, or better still someone he knows there, and take that with you. Also be prepared for US customs to confiscate your drugs - it happened to a friend of mine. You will also have to be prepared to pay, because, as you say, no insurance. But again if you have private health cover talk with them. Just look on it as part of managing you life and what has top be done for you to travel. Don;t let it put you off traveling.
Good Luck
Sailor
So when storm clouds come sailing across your blue ocean
Hold fast to your dreaming for all that you’re worth
For as long as there are dreamers there will always be sailors
Bringing back their bright treasures from the corners of earth. Eric Bogle, Safe in the Harbour