With IELTS, those scores can be used for the US, however, it doesn't go by high band but actual numerical scores, such as you need a 7.0 on the speaking part.
Have you applied to any BON for licensure? You can't sit for the exam until you actually have received permission from a BON to do so. And that can take up to six months for California. New York can take anywhere from two to four months as they have a special verification that has to be done through CGFNS. You also have to apply for Visa Screen.
Did you contact CGFNS by regular airmail? A repsonse will take you forever to get. When did they receive your complete set of documents, including from your nursing school
and licensing board? If not received by mid-April there is no way that they will permit you to sit for the July exam. Did you have prior documentation from them that you were scheduled for July or did you just assume so?
In order for you to take NCLEX in the US, you must be able to obtain a tourist visa and they are not very easy to get right now. You do have the option of flying to Saipan to take the exam, as you can stay for up to three days without having to get a US tourist visa.
Depending on which state that you want to work in, California is taking 8 months for processing petitions to work there. New York is only several weeks.
So right now, you are looking at not being able to take NCLEX for at least several months.