Uber has steadily expanded abroad: it currently operates in 43 countries, with a bulk of the cities located in North America though Uber also operates in dozens of European and Asian cities (it has also been banned in the Korean capital of Seoul).
The smartest option is often to continue health insurance coverage under your old employer's plan, at least until you deliver your baby. Thanks to a federal law called COBRA, you can keep your health insurance coverage for up to 36 months after you leave your job if you work for an employer with 20 or more employees. (If you work for a smaller employer, your state might have a law similar to COBRA that can help you.)
Otherwise, call your insurance company and ask to add your baby to your health plan. You can find the number on the back of your insurance card. Because you have health insurance, your baby has automatic coverage for the first 30 days of life. How nice! Just make sure you sign your little one up within the 30-day window. Yes, after your baby is born, she will be on her own plan with her own deductible.