Is it a prescription that has more refills foreseen in it? That shouldn't be a problem just at a regular pharmacy. Obviously if it's a particularly restricted type of medicine (heavy narcotics) it will be more complicated.
But if it's a prescription that's run out, may need to see a doctor (or the fax confirmation or similar from US doctor).
If you have any doubts - frankly walk into a pharmacy, show them what you ahve and ask what would be needed.
A US prescription needs to be approved by a Canadian doctor before it can be filled in Canada. So the walk-in clinic is the way you need to go. First step is to see a doctor.
It will be dependent on the prescription. For example a few months of birth control likely no problem. Controlled substances, prescriptions that usually require more montitoring or testing will be more difficult. Less likely to be an issue if it is just a prescription for a few months until you can follow-up with your own doctors. Most of the online pharmacies don’t actually service Canadians. Often US citizens are their customers. Ability to use online pharmacies is dependent on province and type of medication.