You are far from too late… .but do not limit your focus to the Ivies…admission to them is a reach for all applicants - everyone is going to have excellent grades, everyone will have excellent scores, recommendations, captain of whatever sport/club…
First look at size of the school - you will find schools with 1500 students here in the States, compared to “small” schools in the UK with 5000; location (urban, suburban, rural, East Coast, West Coast, South…); our version of the Tables is the US News and Reports, look at that as to what schools are most noted for in terms of subjects. Cost, be prepared to pay full tuition as an international student. Politics, the current political climate for international students is not great right now. Keep in mind also that if you intend to practice medicine in the UK, you will still need to attend medical school either in the UK or the US after you spend the 4yrs of money here in the States.
The application process has gotten MUCH easier. The US System called the Common Application is very similar to UCAS, with a few distinct differences. First is cost - each college will charge you an applucation fee of between 75 and 100USD. Second - there is a single essay that is delivered to all the schools you are applying to (picture your Personal Statement)…BUT…each college can ask for supplemental essays.
It is funny, my daughter is leaving the US behind because she does not want to take General Education Classes (required courses that have very little to do with your major but do broaden your perspective is the argument for them), so she is off to Scotland.
Best of luck, feel free to reach out with any additional questions.