You didn't say where you are and how far from the airport you are. Additionally, you didn't say whether you asked BA to deliver the bag to you or if you'll pick it up at the airport.

If you're staying in some Greek island served every other day, then I'm afraid you're up the creek with no paddle (UTCWNP for short). If you're sitting in a resort 3 hours from the airport and you asked for local delivery, then again you're UTCWNP.

As for calling BA to expedite it... it's not gonna work. Sorry. And if you asked for it to be delivered via a courier, then there's a strong possibility it won't get there by Monday. Start looking around for an alternative sourcing of your meds is all I can say, and chalk it up to experience: going forward, if you need medication, it needs to travel in the cabin baggage.