Do I need to take the TOEFL or the IELST to show I am proficient in English?

Possibly. You do need to show that you meet the English requirement. If your prior degree is earned in a country where English is the official language, you do not need additional proof. If English was the language of instruction at the university where you earned your degree, you could provide a letter from the institution stating that English was the instruction language. If you prefer not to take the first and the second routes, you may take TOEFL, IELTS CAE, ESL, or EF SET.