Seeking private duty job, how do I go about it? I do not want to work with an agency.

What experience do you have caregiving for the elderly? You might want to start with an agency to get experience and a reputation for efficient and compassionate and reliable caregiver. Sometimes families will want to direct hire a caregiver they are very happy with. To do this they are usually required to pay a finders fee to the agency.

Also you will need to get malpractice insurance for yourself if you are going to work as a an independent contractor, & a Federal tax ID ( I think )
If you are a RN you can probably get a policy affiliated with the ANA (American Nurses’ Association) sources which are listed in their monthly magazine in the “Ad” section (Journal of thr ANA.)
Good luck!

I want to suggest that you make a profile on Care.com and gain your own, optional clients, on your own schedule. I suggest this site, because a lot of clients on there are not Medicaid, and are clients of families willing to pay the $20-$25 an hour for the services provided to their loved one. Wishing you continuing success!