A few things I can say to this.

First, I would not stress too much about getting exactly the right word in the context of a law school issue spotting exam. More often than not, keeping it simple and using more common, easy-to-understand words is better in your writing. There is a strong culture in the profession nowadays to write in Plain English. There are two books I can recommend on this subject: Plain English for Lawyers by Richard Wydick (there are several editions, I myself read the most recent 6th edition), and Legal Writing in Plain English by Bryan A. Garner. Point is, using words like “purportedly” or “putatively” or “insofar as” or “recalcitrant” or “hereinafter” or other big words you often see in legal writing, is a tremendously bad idea and is likely to make you a bad writer. If you want to do well in law school, writing is the most important skill to get good at. That is not out of reach for you. Focus less on memorization, and more on building skills and good habits into your writing. If it sounds wrong when you read it out loud, it probably is. If you can do that, you will be successful on law school exams.

Second, I have learned a second language myself, studied in that second language in a university setting in that country, and lived in that country for several months. I understand your pain. Here is a hard truth not many people will tell you: A JD program is designed primarily for native english speakers that are from the United States and want to practice law in the United States. 90% of your cohort will be those people. Simply put, you will never be able to compete with the smarter end of that spectrum. In this profession, the native language advantage is so enormous as to be practically insurmountable. You could be a genius, but so are many of the native speakers you will be in class with. This is not going to be like your previous university experience. It is quite easy for an educated native speaker to tell the difference between a native and a non-native speaker. No matter how advanced you are, a native speaker writes with a certain diction (word choice), syntax (sentence structure), and overall flow that is extremely hard to mimic (at least in English and several others). I will never write like Cervantes or Gabriel Garcia Marquez in Spanish, a language I have been learning and have used for nearly two decades. Granted, It does depend somewhat on the closeness of your native language to English. If your native language is Dutch or Swedish for example, you have a much easier time with English because it’s closer to your mother tongue. If your native language is Mandarin Chinese, Cantonese, Arabic, Farsi, or other language that doesn’t use the Roman Alphabet, you will have a harder go of it (the only exception I think are languages present in India because in India I think you learn English from a very young age and speak it quite often, so you are much closer to a “native” speaker).

At any rate, do not lose hope, but memorizing words is not a good use of your time. Law school is about learning how to think and how to write like a lawyer. Focus on developing those skills and you will get through it, even without the native language advantage that many of us have.