If that's a fresh fill with tap water, there's no need to shock. You can't have algae that fast.
You can use trichlor tablets in a floater for a little while, just to build up the CYA. Keep track of how much you put in. 2 lbs of pucks will take your CYA to 30. 3 lbs to 45 CYA. Use no more than that.
Get a drop-type test kit. It's hard to justify a full-blown proper test kit that costs half as much as the pool, but do get something that at least tests chlorine and pH. If you spend a little more, a kit that also has CYA and TA is worthwhile. Just remember that you are somewhat limited in what you're testing, so if things head south, you'll be draining.
Keep tabs on the pH -- those pucks are very acidic, so if you have soft water, you might find pH will get too low and will need adjusting. Once the pucks slow down dissolving, or when you've added enough CYA, you'll need to use bleach. Not a whole lot for a pool your size. Maybe a couple cups a day. That's what the test kit is for, so you know when you need more FC than the melting pucks are adding.
If you haven't already, check out
ABCs of Pool Water Chemistry and then take a gander at the chemistry pages.