There also are phone cards and sim cards sold onboard expressly for use by crew members - these are on the satellite system, either Oceanphone or Harris/Caprock, which are the two companies out there providing service.
Most crew are off at night, and that's when the satellite/internet/phone usage can get pretty intense.
Look into getting a mifi or internet access point you can use in your cabin. Assuming as a doctor, you'll probably have an outside cabin and a porthole, which means a real phone signal will be available. You'll have to do a bit of research to find what works best on the runs that you'll be doing. I have a Virginmobile "broadband to go" hotspot for US ports and a Mifi 2532 for use in Europe. I get pay-as-you-go broadband sim cards in the countries I'm in the most and then switch them out as needed.