You can usually bring your own medicines, if you follow a few rules. Customs officers (CBP) check them at the airport.
Bring no more than a 90-day supply for your own use.
Keep medicines in their original package, with the label showing the medicine name and dose.
Carry a prescription or a doctor's letter in English. The letter should say your name, the medicine (generic name), dose, and why you need it. If the package is not original, the prescription or letter is even more important.
Keep them in your carry-on bag, not checked luggage.
Declare them if the officer asks or the form asks about medicines.
Staying longer than 90 days
CBP says that for longer stays you can have more medicine sent by post or courier, with papers such as a copy of your passport and visa, a doctor's letter and the prescription in English. Many people find it easier to see a US doctor in the first months and get a US prescription.
Some medicines are controlled substances in the US: strong painkillers, ADHD medicines, many sleeping pills and anxiety medicines (for example benzodiazepines). These also follow DEA rules.
Bring only your own, in the original package, with the prescription.
Bring only what you need for the trip.
A medicine that is easy to buy at home may be strictly controlled here.
Medicines not approved in the US
The FDA may allow a small personal supply of a medicine not sold in the US, but it is not guaranteed. Ask a US doctor about a local alternative early.
Marijuana is illegal under federal law, including medical marijuana, even in states where it is legal. Never bring it. It can lead to fines, arrest and being refused entry.
CBD products can contain more THC than the label says. Leave them at home.
Make a list of every medicine with its generic name and dose.
Ask your doctor at home for a letter in English.
Get copies of your prescriptions.
Pack medicines in your carry-on, in original packages.
Putting pills in an unlabeled box or bag.
Bringing a year's supply.
Asking someone to mail you medicines without papers. The package can be stopped.