I transferred into Vanderbilt University after my sophomore year, and only from an unknown state college in FL. I lost 18 credits and had to re-take some prereqs. This caused me to add another year onto my undergrad. Generally they do not care as much about SAT score (still need top 20%) if you have other redeeming factors, and have shown over two years that you are a good college student. Remember, it is still competitive. My transfer class at Vandy had over 2,000 applications and less than 200 got in.
As far as grades go, it depends on where you are now, and where you get in. At my first school I had a 3.66 (Had a 3.3 first sem. that brought it down.) I had other things like great LOR's, multiple academic science scholarships, and I'd been working 30hrs/week. My grades at Vanderbilt were 3.05 first sem, 3.05 second, and around 3.6 this term. The classes here are much harder. People will like to tell you that GPA's are equivalent, but they aren't. I had a hard time adjusting, but I'm doing well now. Unfortunately I will only have a 3.4 by time of application because my first year at Vandy was rough. If you get into a top school and have no trouble adjusting, I don't see why you couldn't get good grades. I have found that I do nearly twice the work for a 3.5GPA here than I would've for a 4.0GPA at the state school. Everyone is different though, and you might not experience such a difference in difficulty. You could keep the 3.6 or even do better if you work hard, as always. If I could go back in time, I would still come here. As far as entering into medical school, your undergrad might help a little, but you can go to University of Nebraska and still get into Columbia. You might be more likely to get in coming from a top 20, but it won't get you in if you have poor stats.