Not a service I’ve seen offered on any of the common providers websites. I’d think the logistics are way beyond anything they could offer. They mostly use “one-hop” drivers between the common stages and have total distance limits. I can’t see how they could maintain medical standard refrigeration and then deliver to the far end of a seven day hop.
Depending on the medication you may do better to research fulfilling a prescription at appropriate intervals.
There are several threads on traveling / obtaining insulin en route and, as I recall, other medications requiring specific storages.
I don’t think it’s a responsibility the carriers are prepared to accept.
Edit: good luck!