Sticky rice is もち米, sold in 1–2 kg bags next to the normal rice. Glutinous rice flour is 白玉粉 or もち粉.
もち米
mochigome · sticky rice grains
白玉粉
shiratamako · glutinous rice flour
もち粉
mochiko · glutinous rice flour, finer
In the shop
Rice corner for もち米; the flour and baking shelf for 白玉粉.
Which shops
Most supermarkets, more of it before New Year. Thai long-grain sticky rice is at Asian grocery shops.
Watch out
上新粉 and 米粉 are made from normal rice, not sticky rice. They won't give a chewy dough.
Lazy Recipe sees that you're in Japan and turns any dish into 3 steps with what Japanese supermarkets sell. Your shopping list shows each item's Japanese label and aisle.