Good questions, if I were to think of it as a starter I would put it in the fridge but you need to use it very soon maybe 7 days. Or make a starter and dump it that will buy you up to 36 hours then fridge for max a week. Just my thoughts.
You can put it back in the frig. Swelling means the yeast are viable and had some nutrient available. When the nutrient is used up the yeast will become dormant if stored at 40°F to 34°F.
The yeast may have been handled improperly to cause the swelling. In this case it is likely a starter should be made before use.