For a list of schools in Santiago, check out the Expat Arrivals page on Education and Schools in Santiago.
Most of the schools listed there will take on kids as young as 2 or 3, so you should be fine with your son.
When it comes to finding a nanny - your best bet would be speaking to other expats and working with their recommendations. Other expats are often one of the most reliable sources of information.
Alternativley try the website greataupair.com, they have a portal where you can list your requirements and they will try to find you a match.
I'd also recommend you check out our page on Kids in Santiago for more information of child-related issues.
I hope this information helps. Good luck.