This is not accurate (but $200K is the professional degree limit for federal loans.) The lifetime FEDERAL loan limits are $257,500 including undergrad/grad/professional degrees. That number excludes the $65K max parent plus loans.
OP, you will need to do research on loans. This area is developing rapidly, and will look different by the time you go to med school. Here is a thread on the current loan change info: Loan changes effective 2026-2027 academic year
Right, all private loans are not predatory. For example, Sallie Mae offers educational loans for med school. Some med schools offer loans to their students, and more are expected to begin doing so. Some states are offering loan options for med school students. Again, things are rapidly developing.
As many posters have said, I would recommend you minimize undergrad cost and take out no more than the $27K max in federal loans for undergrads.