Your 2nd hour starts after you have finished the bottle of water with the sugar calories in it. You have to always wait 1 hour after the flavorless calories whatever they may be. oil-sugar-or both.
You may drink as much plain water as you want, all of the time. There is no period that you can't.
I take 2 TBS oil in the morning upon waking, wait one hour, drink lots of plain water during that time. And when the hour is up, I may have breakfast or whatever.
by the name of your nickname (tired mom) I hope that shangri-la will give you back the energy that you need when you lose some weight.
If you are actually tired, as your tag implies, always remember to check how much starch may be in your daily diet. Too much and in the wrong balance leads to fatigue and overweight.