A.C.
I agree with S.S.--kids this young need human interaction and are really not capable of "playing by themselves" too well. Plus, at this age, they start doing a lot of silly things (climbing places they shouldn't, getting into stuff they shouldn't, etc.). So, it's also not a safe thing to leave them unattended for very long.
See if you can "nanny-share" (go in with another family to pay for a nanny) or find a SAHM who is doing childcare or a small in-home childcare situation. Or put him into childcare. Yes, he'll get sick, but he'll get sick regardless (now or later or both), and there's not much you can do to prevent that unless you all live in a bubble. :)