I do not think that foreign trained Nurses can apply for H1B. The only nurses that can apply for H1B are those trained in the US with BSN degree. Even the US trained nurses with just the Associate degree are not able to apply for H1B though they might have passed RN licensing exam.

As far as applying for GC, due to Visa Backlog, even this avenue is closed as of right now. The Democrats tried to pass a bill to recapture some unused visas for Nurses but was defeated by the Republicans in the Senate. However, it is best to consult with an attorney.