Can I apply for a health certificate with a social security card?

If you don't have an ID card, you can use a medical insurance card, because there are ID numbers and personal photo information in the medical insurance card. Generally, as long as you can record your ID number and check your personal photo information, you can use it to apply for a health certificate.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.