import restrictions are generally federal
Federal law has unfortunately restricted all "prescription" medications in the USA since around 1950. Generally, no sales or imports are allowed without a valid prescription from a licensed practitioner.
The same rule applies nationwide, although different states have different licensing standards for who can prescribe. (I have heard that some states allowed barbers to prescribe, but even if you have a PhD in pharmacology you are not allowed to buy without a prescription from your barber or whoever is allowed to prescribe.) The diligence of Customs and Postal inspectors might vary from one region to another, but the import law does not.
Beginning around 1988, partly in response to pressure from AIDS activists who wanted to take medications that the US FDA had not yet approved, FDA allowed imports of a 90-day supply for personal use without a prescription. However, the current Republican administration has unfortunately repealed that, and the Republican party is in general very hostile to imports of prescription drugs. FDA claims it's because they can't guarantee the safety of drugs made elsewhere, and Republicans in Congress claim it's because someone might import anthrax, but the real reason is almost certainly campaign contributions from drug companies that want Americans to continue to pay full price rather than importing from less expensive markets.
One solution would be to repeal the prescription requirement, but neither party is proposing that currently. To the contrary, prescriptions have become so profitable to licensed prescribers that the requirement is producing its own lobbies. In the 1990s, it was extended to magnifying glasses above a certain power. Sherlock Holmes would no longer be allowed to buy or import his magnifying glass without a prescription, presumably from an ophthalmologist but maybe from a barber.
As for the safety rationale, one need only look south to Mexico, where it is generally legal to purchase "prescription" medication regardless of whether you have a prescription. (Insurance companies might require a prescription as a condition of reimbursement, but the law generally does not require one as a condition of sale.) Life expectancy is almost the same as in the U.S.A. but people spend less than a tenth as much on healthcare. It seems fairly clear that the main reason for requiring prescriptions is that the added costs go to 'special interests' (prescribers) who lobby for more prescription requirements, just as the import restrictions are supported by pharmaceutical companies that charge more for the same products in the U.S. than elsewhere. The prescription requirement creates a pretextual safety rationale for confiscating imports, regardless of whether they are approved or whether their patents have expired.
"Those who like sausages and respect the law should not watch either being made." - Otto Von Bismark
