I was in Sri Lanka during August and, yes, I got bitten by mosquitoes. The worst place was in the south-west around Weligama and Unawatuna. Kandy, Nuwara Eliya and Ella weren't too bad as the climate is slightly cooler up in the mountains. The mosquitoes would generally appear during the late afternoon/evening which, for me, made sitting outside during those times a bit irritating. Take plenty of repellent with you, cover up and, if you're at a hotel or restaurant, ask the staff if they can burn citronella to keep the critters at bay. Buy one of those plug-in devices for your room. Drink lots of gin and tonic (or just tonic water - mosquitoes apparently hate the quinine).
The chances of you getting dengue fever are fairly low. I got eaten alive by mosquitoes during a recent 4-month trip to Asia and was absolutely fine, other than the itching!