Well, welcome to the US. I hope you enjoy it here and get to do some exploring. 😀
It does seem more practical to have your medication managed here in the US. Ideally, when you arrive you would select one doctor to serve as your general physician (called a Primary Care Provider or PCP). You would go to this doctor for almost all of your medical needs -- annual wellness exams, typical illnesses, medication management, etc. Depending on the severity of your asthma, you may have this doctor recommend a pulmonologist who would focus on your asthma care. Either one of those doctors could prescribe and monitor your asthma medication.
I am not 100% sure on this, but I believe the laws surrounding prescriptions vary by state because of medication abuse. In some places, they cannot give you a hard copy. It would be best to discuss this with the doctor who is prescribing, or with the pharmacist. Tell them you are new here and ask them to explain what your options are.
Also, will you have health insurance coverage while you are here? I know some inhalers can be costly, even with coverage. can probably give you more insight on this.
Best of luck, let us know what other questions you have. -Melissa, asthma.net team