In the DO world, there are some free-standing medical schools (even if they call themselves a university), and there are medical schools that are part of a larger university system (ie MSU, OSU, NSU, UMDNJ/Rowan, etc). For schools that are part of a larger university system, you will have to check on the university's stance on enrollment of undocumented students. For the stand-alone schools, you will have to contact each individual schools to find their policy.
You have a very tough road ahead of you with a lot of potential roadblocks.
1. Getting into medical school
2. Obtaining financial aid (since federal loans are probably unlikely, and not sure if private banks are willing to loan the equivalent of a mortgage to an undocumented student who will have difficulty obtaining work)
3. Obtaining a residency (you need at least 1 year to get a license in most states). Residents are "employees" who have to go through HR, fill out W2, and I-9 forms verifying that you are allowed to work (and soon, e-verify might be required). A lot of residencies are at university hospitals where part of the training will occur at the VA Health System (so additional federal background checks, fingerprints, photos will be required of the residents before starting). It's also will be difficult for you to get a H1B visa or J1 visa for residency because you're physically here in the US. You will need to back in your home country to process the H1B or J1. And as soon as you leave the US, it will trigger an automatic 10 year ban before you are eligible for H1B, J1, or even a tourist visa.
4. Obtaining a unrestricted license - each states will have their unique requirement, but they require a lot of documentations. Some even ask for undergraduate transcripts. All will ask for med school transcripts, residency verification, and letter of good standing from all hospitals that you have ever worked in, and a letter of good standing from all states that you have held a medical license. Some require an extensive background check.
5. DEA license - you will need a DEA registration number in order to prescribe certain drugs (and to work in certain industries).
6. Finding an employer who is willing to hire an undocumented worker (and face the consequences/fines of an ICE raid). Or you can open your own practice - but you will need a lot of starting capital to fund your practice, plus you will need to apply to the state to be a medicaid provider, and to HHS for a medicare provider, plus each insurance companies that you will want to participate in. You can take "cash" but then as a cash business, you better have a good accountant because cash business are always on the radar of the IRS (plus physician cash practice raises the DEA suspicion for being a pill mill)
It's a difficult road, with many hurdles. A bona-fide marriage to a US citizen can help. Congress passing the DREAM act can help. I recommend that you discuss all your options with an immigration attorney so you will know your options, and also the possible impact that any action can have (ie would doing this jeopardize your chances of obtaining that, etc).
For a source of inspiration, check out the life story of Alfredo Quiñones, MD. He was a Mexican illegal migrant worker in California. He eventually went from night classes at a community college to UC Berkeley, to Harvard Medical School, to a UCSF residency in neurosurgery, and now he is an assistant professor of neurosurgery at Johns Hopkins. He was able to gain legal status thanks to President Ronald Reagan amnesty program (he obtained a work authorization, then a green card when he was at Berkeley, and became a naturalized US citizen when he was at Harvard).
