I work in health insurance in the US and here’s how it goes:

You go to your doc, they write you and Rx and you take it to the pharmacy. The pharmacy runs it thru your insurance and insurance pays.

Let’s say your doc writes an RX for 30 pills for 30 days. You can generally get a refill (if you have any left on the prescription) 1-2 days before your next refill is due. But if you try to get another refill 15 days after the first your insurance won’t pay.

A pharmacy can dispense medication with a valid rx, you don’t need insurance to get the meds. Honestly your best bet is to go the the manufacturer of the meds to see if they have copay assistance.