It's never too early to add chemicals, particularly chlorine. Pop one in the floater and let 'er rip. Do get your test kit ASAP (like tomorrow) and check your Cl and pH. Get the 5 way hth kit, that will take care of most of your needs. Do all the tests, except the CYA test (you won't have any of that built up in the water yet anyway) and post them here.

And yes, go swimming!

Michael