Part of your difficulty is that you don't really seem to have a structure in the essay, which makes it difficult to think of what to say. The main technique which will help you expand your paper is developing a clear structure and then closely researching and thinking about each section.
First it would help if you divided the paper clearly into subheadings. Your introduction, after setting out your thesis, should include a few transition sentences describing how you will be supporting your thesis and in what order.
Your first section, with the heading "Emma Lazarus: Themes and Context", should give a brief overview of Lazurus' background and cultural context. It should also very briefly summarize the main points in her poem about immigration.
Your next section might use the heading "Claude McKay: Themes and Context". It should discuss McKay, his island background, his early experiences in the United States, and summarize the attitude found in his poem.
Your next section might focus on literary technique. Both writers are using convention verse forms, following the traditional British models which were followed by many American poets. You might look at why they did this. Lazarus, for example, could have chosen Whitmanesque free verse, but did not, and McKay could have delved into island tradition or African-American traditions in writing, as did many of his contemporaries in the Harlem Renaissance. Thus in a section on literary techniques you should examine how this sort of cultural assimilation reflects their visions of immigration.
After this, you could insert one section focusing on race and then the very nice material you have on gender, followed by your material on attitudes towards America and your conclusion. Having this sort of clarity of structure, and using headings to clearly separate themes, will make adding material much easier.