Is possible for me to have a remote research internship with an ivy league professor.

First, it's already the end of June, so if you wanted a remote internship prior to 12th grade, you should have lined up 6 months ago over Winter break. Second, unless, you personally know an Ivy professor as a family friend and that family friend is in need of someone who can do some grunt work for free, it's highly doubtful that by writing emails or cold-calling you'd get very far in this endeavor.

I think it makes more sense to contact professors that are living within a driving distance of your house who have internship possibilities at Texas colleges. Perhaps you know some friends of family members who can introduce you and set up a one on one information session.

99.9% of internships with professors at elite colleges only happen to high school students if they have some prior connection with the school through their parents who may be faculty members or connected to higher ups in the college administration who are willing to make an introduction if they know that that certain student is 100% keen on applying their ED/EA and not wasting their time.

Most academic internships occur after your first year of college through the help of the college counseling liaising the introduction or through job postings on the college's internal websites etc.

Good luck.

I seriously doubt that IVY League professors offer internships to high schoolers let alone anybody who is not affiliated with the college. If you want to go into the Med Field, I would try to do research or something like that. Also interning under a professor would be very unlikely to massively improve your chances of getting in.