The last part is not true. Yes when you are on student visa, you are a student and are not supposed to work. But if you want, after a certain amount of time (that varies) can request your uni/college to let you work. Then you can be given two options. Either to work within the premises of college, which is handy too, or can be allowed to work externally. The rear may not be that easy to get but many colleges give this permission to the students after a certain amount of time.
Other than that, its US, so in worst case you’ll get a odd job anywaz even if you dont want to let your college know. HTH.