To use cold tea bags as a compress, soak a tea bag in clean water and then place in the refrigerator for 30 minutes. Then, place the tea bags on your eyes. Leave for 10 minutes or so twice daily before removing and rinsing the area with warm water. Source.
September to October is the rainy season in Langkawi and this is the period which most tourists like to avoid. But the fact is even during the rainy season, it rains only for about 2 hours a day but usually in the late afternoon and at night.
Cairns climate long term averages. If you're not a fan of the tropical heat like in Thailand and Bali then the best time to visit is from around April to October when temperatures drop. Generally the temperature only drops enough to require a light jacket or cardigan at night- you can leave the winter coats at home.