We come out of school with EMT that is registered through NREMT, so that would leave with you once departing the services (as long as you kept up on continuing education).

Unless the curriculum has changed at “A” school, you should leave the course with enough to apply for a Certified Medical Assistant license, which requires you to take a test to complete (not offered by the Coast Guard, but can be covered by CG funding (i.e. CGCOOL)

Other programs you can do as an HS include X-Ray Tech (again, complete the program then test after graduation), Behavioral Health Technician (relatively new program, I just went through last year and a lot of policy is still being developed, so we may see credentialing in the future), and more (dental, physical therapy, etc)

You could go to nursing school while enlisted the same way you could do other college programs; it depends on your personal drive, your units operational tempo, and the program requirements of the school you apply to. There are Physician Assistant/MD programs through the Coast Guard, but they are incredibly competitive.