If you will only have undergraduate debt, and your parents can afford to pay 200K for medical school, you should look at realistic levels of debt for yourself.
Do you think 10K per year of student loans would be acceptable to you? In that case, would your parents agree to pay 10K per year for undergrad and you take out 10K of loans per year?
If not, remember that many schools that might offer free tuition won’t offer room and board, and your costs will likely be at least 10K per year.
Have you looked here? I’m not sure if you would qualify, but there are a lot of them.
http://www.finaid.txstate.edu/scholarships/freshman.html
I’m also wondering if the OP’s parents realize how few colleges are less than 10K per year, especially considering only a few offer full rides including housing and books. And you also need a college that has pre-med courses available - if you can’t take organic chemistry at a college, the low cost doesn’t help.
My take on this is that the parents want to have control over the OP, but without a contract that says the parents will pay for medical school, they are not obligated to do so.
I’d rather say this to my kid: I can pay up to 200K for your undergrad and grad school, but past that point, you have to take out loans for the difference. So if it is 80K total for undergrad, you’ll have 120K left to pay for medical school.
Have your parents read this:
https://www.aamc.org/students/aspiring/paying/283080/pay-med-school.html
And - how about a 6 (3 + 3) or 7 year (3 + 4) med program? These can result in quite a bit of savings (one year of undergrad tuition generally).
http://www.utdallas.edu/pre-health/ut-pact
http://som.uthscsa.edu/Admissions/earlyMatriculationProgram.asp
Perhaps some negotiation with your parents is in order, or more creative thinking. If you are sure you want to go to medical school, a 7 year med program might be a good idea.
Texas A&M seems to allows juniors to enter medical school, but it is more iffy than a 7 year med program.
http://medicine.tamhsc.edu/admissions/faq.html