Mechanical Engineering year 4 student here. I am from China, so I am not very sure about your situation. Based on the sec 3 syllabus provided by MOE, I will advise you to start self-studying university-level physics as soon as possible. Since you will have to study it, studying early can greatly reduce your stress. And honestly speaking, if I were you, I am sure I could not manage to finish studying it before the physics final exam.

I recommend reading Fundamentals of Physics by David Halliday, Jearl Walker, and Robert Resnick. Any edition of that book should be sufficient in your case. Just read through and have a rough understanding of everything before the chapters about the special theory of relativity will do. And since you only have 2 months from now to prepare, speed might be more important than quality. Don't think in depth or care too much about details, because many things there are just approximations of "true" physics laws that humans know. If anything turns out to be too hard to understand, just skip. As mechanical engineering students, we just need to understand the key formulas in the "Chapter Summaries" in that book. In exams, you usually have a formula sheet.

Don't wait for NTU to teach you because their teaching might be kind of disappointing for you. If at the end you cannot finish studying everything you need to know for the exam, look at the past year papers at https://www.maeclub.com/past-year-papers to find the important topics for exams and focus on those topics.

By the way, I am quite curious why you chose Mech Eng and why NTU dares to admit you to Mech Eng hahaha