There are a few institutions which offer medical programs, among them: The Tel Aviv University, The Hebrew University, The University of Haifa, the Ben Gurion University and more. In order to study medicine in Israel you must first complete your pre med studies. Candidates need to present a GPA of at least 3.4. and MCAT scores (or their equivalent in case students are not from the US) with scores of above 27.
Regarding the psychology programs - There are a few institutions in Israel which offer a BA program in psychology, among them: IDC Herzliya which offers a full BA track in psychology that also includes communications, government, business administration or social thought, The University of Haifa which offers a semesterial program, The Hebrew University of Jerusalem which offers a special program in which the students take the first year classes in English and at the same time study Hebrew at an Ulpan so the next years could be in Hebrew and more.
I've attached a link at the end of my message to an article about the different institutions that offer a BA in psychology and the different programs you can choose from.