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Raspberries (and blackberries and all those similar) have a short shelf life which is why you rarely see them sold in stores. They might last a day or two but go bad fast (even with refrigeration.) Blueberries also go bad quickly but can last a bit longer. Yes, refrigerate them, but don't wait too long to eat.
Store in the refrigerator to keep fresh for up to 10 days. How long depends on the variety of berry, but blueberries will stay fresh the longest. Tip: Berries are one of the most perishable fruits because they're so thin-skinned.