Shields state that they are carried in one hand, so you would only have a single hand free. Longbows, shortbows, light and heavy crossbows all have the two-handed property which means they require two hands to use, so no they could not be fired while using a shield. You could, however, wield a dart, sling, blowgun, net, or hand crossbow and still use a shield. There are also some one-handed thrown weapons which I have not mentioned.