My sibling slow selling rental prop for NH financing. I am sole live in 24/7 caretaker almost 3 years. Burned out. Can I legally force him?

Your question indicates that you have provided care for over two years, but you believe the time has come for institutional care in a nursing home. Is your question directed toward obtaining Medicaid payment for long term care in a nursing home?

Are you taking care of a parent? One exception to the Medicaid transfer rules is the "Caregiver Exception" that allows transfer of a persons residence to a son or daughter who has provided care for more than 2 years. Section 1396p(c)(2)(A)(iv):

https://www.law.cornell.edu/uscode/text/42/1396

Another exception to Medicaid eligibility rules on countable assets allows an applicant to hold onto income producing property.  Could the rental property fit into this category?

Your question indicates that a conversation with an elder law attorney in your state would open up many options for long term care resources, and Medicaid eligibility.