There is a website I've used and found great jobs in the States as well as in Switzerland. It is called greataupair.com which allows you to connect with caregivers of various types while selecting the language requirements etc.
Click on "hire", then "senior care" and on the left select "language options".
Besides several other search refinements, you can select Paid experiences as well as certifications:
Certified Nursing Assistant
Senor Care Companion
Hope this helps.
All the best with your move to Milan!