The short answer to this question is maybe.
If you are married or were married but divorced, and your spouse paid into the Social Security system via payroll taxes or self-employment taxes, you will qualify for a reduced benefit, generally 50% of the spouse's benefit amount, when you reach your retirement age. In the case of divorce, you must have been married 10 years or more, you must not be remarried, and your ex-spouse must have made contributions based on their work history.
If you were never married, or married but neither spouse made contributions via payroll taxes or self-employment taxes, you will not be eligible to collect any Social Security benefits.
To be eligible to collect Social Security benefits, you need at least 40 quarters (10 years) of work that was taxed for Social Security.
You can continue to work and collect Social Security benefits, if eligible. If you have reached your full retirement age (65 - 67 depending on your date of birth) you can earn up to $46,920 without any reduction in your benefit amount. If you are between 62 and your full retirement benefit age, the benefit reduction kicks in when you earn 17,640 or more (2019).
Benefit amounts are determined by your average monthly earnings over your highest paid 35 years of work. It is important to note that if you worked less than 35 years paying into the system, your benefits are still determined by taking the earnings reported and dividing as if earned over 35 years. So it is to your benefit in the long run to work and pay your payroll taxes at least 35 years before claiming your benefit. How does this work?
Say you are never married and only worked 12 years on the books, and you averaged $40,000 annually over those 12 years. You reached your full retirement age in 2019 and file for benefits. Your average monthly earnings would work out to $1,142 (40,000 x 12, divided by 35 years, then divided by 12 months). Your average monthly benefit payment would be $902.
Now say you are never married and worked a full 35 years on the books, and you averaged $40,000 annually over those 35 years. In this scenario your monthly benefit payment would be $1,603.64. That is a tremendous difference every month for the rest of your life! Considering that women who reach full retirement age before claiming Social Security benefits are expected to live an additional 22 years, the difference in retirement benefits over your lifetime by working on the books your entire nanny career is a whopping $185,000!
This is a complicated subject, and given the vital importance your retirement income will play in the last two decades of your life it is a subject you should take the time to understand. The Social Security Administration maintains a special portal for women to help you understand how your actions in the workforce today will impact you tomorrow.