Direct payments

I have experience with managing direct payments because I did this for my daughter some years ago. Yes, you can use an agency but they may charge you extra for requesting the payments from your local Authority. (council)

The better option in my opinion is to ask your local Authority to manage them for you. There's some information here.

https://www.nhs.uk/conditions/social-care-and-support-guide/money-work-and-benefits/personal-budgets/

If it's determined that care/support is needed you will also need a financial assessment because many people have to pay a contribution towards the care they receive.