As others have said, this appears to be a scam, and you should contact your bank to see if there is any chance of tracing or retrieving your funds.
If you paid cash that is a red flag all by itself and the money is almost certainly irretrievably gone.
If you are still interested in traveling to the United States, the visa application process is outlined at https://ng.usembassy.gov/visas/
For applicants within Nigeria, the above linked page shows that
In the country you selected, visa applications and interview scheduling are primarily facilitated by a third-party company, U.S. Travel Docs. Please visit their website at: https://www.ustraveldocs.com for additional information on determining what visa type is best for you and how to apply.
Digging further, I find that as of 2024 the nonrefundable visa application fee is payable online directly to that handling company or in person via a specific form at a GT Bank branch.
In particular note that, the US Department of State has issued a fraud warning about scammers targeting US Visa applicants: https://travel.state.gov/content/travel/en/us-visas/visa-information-resources/fraud.html which says (about the Diversity Visa process) in part
Also avoid visa consultants who charge money because they claim they can improve your chances of winning. We do NOT work with consultants and they CANNOT improve your chances of being selected.
and also
Some websites and emails try to mislead customers and members of the public into thinking they are official U.S. government websites. These websites are designed to appear official, and often have images of the U.S. flag, U.S. Capitol, White House, or Statue of Liberty. What these websites and emails are missing is the “.gov” suffix on their addresses. Remember that anything that does not end with “.gov” should be considered suspect
While there appear to be a variety of legitimate visa assistance services (in general, charging a fee to help you fill out your visa application correctly and with an eye to a successful outcome) and travel agents that also offer visa services in Lagos and elsewhere in Nigeria, the legitimate ones would not claim to be US Embassy staff, and US Embassy staff do not arrange commercial flights.
Note: It's not completely impossible that you purchased a nonrefundable plane ticket from a legitimate travel agency, who attached proof of round trip airfare to a visa application they submitted on your behalf to improve your chances of acceptance. (While this is a common misconception, the US State Department directly states Do not make final travel plans or buy tickets until you have a visa.) Even if you were merely confused into thinking that you were dealing directly with the US Embassy, in that case you should have a receipt where you signed your acceptance of such terms -- and having signed those terms, you would have no recourse, and the money is equally gone.