Milk in a small sealed bottle will it go bad if stored in cool pantry?

That depends how cool the pantry is and for how long the milk is stored there. If it is as cold as a fridge, then it would spoil at the normal rate - perhaps sooner if the container was not sanitized before filling. The warmer the pantry, the faster the milk will spoil. Generally, potentially hazardous food should not be unrefrigerated for more than 2 hours, but less time is better. Cut that to one hour if the ambient temperature is around 90°F.

If no refrigerator is available, use a frozen cold pack to keep the milk cold.