Most of this question is really a series of questions for your US health insurance provider - will they pay bills for medicines prescribed by a foreign doctor or not? From Canadian pharmacies (don't see why not, but don't know)? Note that you'd mostly be paying out of pocket and getting reimbursement.
You may run into issues with 'out of network' doctors and providers that in some situations may mean you need to go to USA.
As for the Rx itself: go and see a pharmacist in Canada on arrival, preferably not one of the big chain ones (although they can vary quite a lot, some of the big chain ones are ok, some of the smaller pharmacies are great, some are not, some primarily work on specific niches). And then ask the pharmacist how long they will honour the US prescription, and could they possibly re-up?
And note, this could depend on the specific medicines and Rx - particularly rare/expensive may be more of a problem, and some that are considered narcotics (for obvious reasons), and some other specific scheduled ones (eg that are mostly or only done for severe chronic conditions/in hospitals, because they may be paid for by provincial plans in Canada).
Oh - and some things are over the counter in Canada that arent' in the USA and vice versa. I have heard that some things can be limited for US customers because they're scarce at times here (because much cheaper and US customers tend to buy them up).
It's possible some pharmacists at border regions will be more flexible or used to this. Don't know.
I have an acquaintance who gets coverage through work in the USA (and commutes basically). Biggest gap is basically for some specialized consutlations that are typically not covered by provincial programs, because the US plan requires those consultations to be 'in network.' But I've no idea if this is the type of thing you'd encounter, will just depend on your plan. Overall their US insurer doesn't mind because basically the provincial plan covers the vast majority of actual medical expenses, it's a bargain for the insurer. That doesn't mean they're flexible about their rules, though.
