The short answer is no, the F visa is a student visa so it will not allow you to work in the US. A student on an F1 visa needs to show that they can support themselves while studying in the US without a job so they are subject to strict work restrictions. The F2 is even more limited than the F1 because it is only for the dependents accompanying a student who is on an F1. Children on an F2 can attend school but a spouse on an F2 can not work or study.
If you do want to work you can get a H1B visa but to do that you would first need a US employer to sponsor you and your job would need to be a “specialty occupation.” Generally a specialty occupation is one that requires a specialized knowledge, things like engineers, doctors, business professionals, etc. You will also need to show that you possess any necessary degrees and can meet the education requirements of the job that you seek.
If you are not looking to work in a specialty occupation, you do have other options but I suggest that you speak with an immigration attorney about what would work best for you. An experienced immigration attorney will be familiar with the process so will be able to work with you to determine your best option.
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