Is there any assistance available for a relative of elderly person?

Majority of grown children do not get paid for caring for their parent, unless the parent is financially able to pay from their own pocket. If a parent can afford to pay you, the parent might as well hire a certified trained caregiver… thus allowing you to keep a full-time job so that you can add to your own retirement.

If your parent qualifies for Medicaid, the State might allow a trained Caregiver from an Agency to come in to help a couple hours a day. Check to see if your State has “Cash and Counseling” program. Note that each State has their own rules, regulations, and programs. Some have waiting lists.

As for a social life for Mom, contact your local council on aging.... if you live in the States, go to the website link below.... click on your State.... now click on the city/county. The agency should be able to direct you. https://www.agingcare.com/local/Area-Agency-on-Aging

No, there is no recovery for lost wages caring for Mom. If there was, many of us here would be filthy rich.
As for activities, try your local senior center or your county office of the aging.